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DTSTART;TZID=America/New_York:20210913T090000
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DTSTAMP:20260504T140042
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UID:10000053-1631523600-1652461200@cmsa.fas.harvard.edu
SUMMARY:Swampland Program
DESCRIPTION:During the 2021–2022 academic year\, the CMSA will host a program on the so-called “Swampland.” \nThe Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory\, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology\,  which has led to a great deal of activity in the field in the last years. \nThe Swampland is intrinsically interdisciplinary\, with ramifications in string compactifications\, holography\, black hole physics\, cosmology\, particle physics\, and even mathematics. \nThis program will include an extensive group of visitors and a slate of seminars. Additionally\, the CMSA will host a school oriented toward graduate students. \nMore information will be posted here. \nSeminars\nSwampland Seminar Series & Group Meetings \nProgram Visitors\n\nPieter Bomans\, Princeton\, 10/30/21 – 11/02/21\nIrene Valenzuela\, Instituto de Física Teórica\, 02/14/22 – 02/21/22\nMariana Grana\, CEA/Saclay\, 03/21/22 – 03/25/22\nHector Parra De Freitas\, IPHT Saclay\, 03/21/22 – 04/01/22\nTimo Weigand\, 03/21/22 – 03/28/22\nGary Shiu\, University of Wisconsin-Madison\, 04/03/22 – 04/10/22\nThomas van Riet\, Leuven University\, 04/03/22 – 04/09/22\nLars Aalsma\, University of Wisconsin-Madison\, 04/11/22 – 04/15/22\nSergio Cecotti\, 05/08/22 – 05/21/22\nTom Rudelius\, 05/09/22 – 05/13/22
URL:https://cmsa.fas.harvard.edu/event/swampland-program/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260504T140042
CREATED:20240213T112446Z
LAST-MODIFIED:20240502T160729Z
UID:10002496-1631698200-1653474600@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium 9/15/2021 - 5/25/2022
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a Colloquium\, organized by Du Pei\, Changji Xu\, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/26/2022\nSamir Mathur (Ohio State University)\nTitle: The black hole information paradox \nAbstract: In 1975\, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997\, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center\,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox\, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown\, using some theorems from quantum information theory\, that these extrapolations were incorrect\, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines\, with a postulate that information would leak out through wormholes. Recently\, it was shown that this wormhole idea had some basic flaws\, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle. \nVideo\n\n\n2/2/2022\nAdam Smith (Boston University)\nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.\n\n\n2/8/2022\nWenbin Yan (Tsinghua University)\n(special time: 9:30 pm ET)\nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory. \nVideo\n\n\n2/16/2022\nTakuro Mochizuki (Kyoto University)\nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract: In 1960’s\, Narasimhan and Seshadri discovered the equivalence\nbetween irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles\nand stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.\n\n\n2/23/2022\nBartek Czech (Tsinghua University)\nTitle: Holographic Cone of Average Entropies and Universality of Black Holes \nAbstract:  In the AdS/CFT correspondence\, the holographic entropy cone\, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual\, is currently known only up to n=5 regions. I explain that average\nentropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily\, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average\nEntropies” (HCAE). I conjecture the exact form of HCAE\, and find that it has the following properties: (1) HCAE is the simplest it could be\, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture\, the extremal rays of HCAE represent stages of unitary black hole evaporation\, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel\, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n\, namely its bounding inequalities are n-independent. (6) In a precise sense I describe\, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.\n\n\n3/2/2022\nRichard Kenyon (Yale University)\n\n\n\n3/9/2022\nRichard Tsai (UT Austin)\n\n\n\n3/23/2022\nJoel Cohen (University of Maryland)\n\n\n\n3/30/2022\nRob Leigh (UIUC)\n\n\n\n4/6/2022\nJohannes Kleiner (LMU München)\n\n\n\n4/13/2022\nYuri Manin (Max-Planck-Institut für Mathematik)\n\n\n\n4/20/2022\nTBA\n\n\n\n4/27/2022\nTBA\n\n\n\n5/4/2022\nMelody Chan (Brown University)\n\n\n\n5/11/2022\nTBA\n\n\n\n5/18/2022\nTBA\n\n\n\n5/25/2022\nHeeyeon Kim (Rutgers University)\n\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/15/2021\nTian Yang\, Texas A&M\nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.\n\n\n9/29/2021\nDavid Jordan\, University of Edinburgh\nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.\n\n\n10/06/2021\nPiotr Sulkowski\, U Warsaw\nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.\n\n\n10/13/2021\nAlexei Oblomkov\, University of Massachusetts\nTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane. \nAbstract: The knot homology (defined by Khovavov\, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However\, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details\, using physics ideas of Kapustin-Rozansky-Saulina\, in the joint work with Rozansky\, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane\, the symmetry is the geometric counter-part of the mentioned Poincare duality.\n\n\n10/20/2021\nPeng Shan\, Tsinghua U\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.\n\n\n10/27/2021\nKarim Adiprasito\, Hebrew University and University of Copenhagen\nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.\n\n\n11/03/2021\nTamas Hausel\, IST Austria\nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.\n\n\n11/10/2021\nPeter Keevash\, Oxford\nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.\n\n\n11/17/2021\nAndrea Brini\, U Sheffield\nTitle: Curve counting on surfaces and topological strings \nAbstract: Enumerative geometry is a venerable subfield of Mathematics\, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s\, in particular\, the interaction with String Theory has sent shockwaves through the subject\, giving both unexpected new perspectives and a remarkably powerful\, physics-motivated toolkit to tackle several traditionally hard questions in the field.\nI will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X\, D)\, with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X\, D)\, including the log Gromov-Witten invariants of the pair\, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety\, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds\, the Donaldson–Thomas theory of a class of symmetric quivers\, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.\n\n\n12/01/2021\nRichard Wentworth\, University of Maryland\nTitle: The Hitchin connection for parabolic G-bundles \nAbstract: For a simple and simply connected complex group G\, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks\, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.\n\n\n12/08/2021\nMaria Chudnovsky\, Princeton\nTitle: Induced subgraphs and tree decompositions \nAbstract: Tree decompositions are a powerful tool in both structural\ngraph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. \nTree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.\n\n\n12/15/21\nConstantin Teleman (UC Berkeley)\nTitle: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system \nAbstract: I will present a construction of the object in the title which\, applied to the classical Toda system\, controls the theory of categorical representations of compact Lie groups\, along with applications (some conjectural\, some rigorous) to gauged Gromov-Witten theory. Time permitting\, we will review applications to Coulomb branches and the categorified Weyl character formula.
URL:https://cmsa.fas.harvard.edu/event/cmsa-colloquium_2021-22/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220124T090000
DTEND;TZID=America/New_York:20220521T170000
DTSTAMP:20260504T140042
CREATED:20230904T083438Z
LAST-MODIFIED:20240215T103430Z
UID:10000055-1643014800-1653152400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program
DESCRIPTION:During the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses\,  a conference\, and a workshop. \nGeneral Relativity Mincourses: March–May\, 2022 \nGeneral Relativity Conference: April 4–8\, 2022 \nGeneral Relativity Workshop: May 2–5\, 2022 \n  \nProgram Visitors \n\nDan Lee\, CMSA/CUNY\, 1/24/22 – 5/20/22\nStefan Czimek\, Brown\, 2/27/22 – 3/3/22\nLan-Hsuan Huang\, University of Connecticut\, 3/13/22 – 3/19/222\, 3/21/22 – 3/25/22\, 4/17 /22– 4/23/22\nMu-Tao Wang\, Columbia\, 3/21/22 – 3/25/22\, 5/7/22 – 5/9/22\nPo-Ning Chen\, University of California\, Riverside\, 3/21/22 – 3/25/22\,  5/7/22–5/9/22\nMarnie Smith\, Imperial College London\, 3/27/22 – 4/11/22\nChristopher Stith\, University of Michigan\, 3/27/22 – 4/23/22\nMartin Taylor\, Imperial College London\,  3/27/22 – 4/11/22\nMarcelo Disconzi\, Vanderbilt\, 5/9/22 – 5/21/22\nLydia Bieri\, University of Michigan\, 5/5/22 – 5/9/22\n\n 
URL:https://cmsa.fas.harvard.edu/event/general-relativity-program/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Program-Banner_800x450-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220301T100000
DTEND;TZID=America/New_York:20220517T130000
DTSTAMP:20260504T140042
CREATED:20240215T103842Z
LAST-MODIFIED:20250328T144509Z
UID:10002743-1646128800-1652792400@cmsa.fas.harvard.edu
SUMMARY:General Relativity Program Minicourses
DESCRIPTION:Minicourses\nGeneral Relativity Program Minicourses \n\nDuring the Spring 2022 semester\, the CMSA hosted a program on General Relativity. \nThis semester-long program included four minicourses running in March\, April\, and May;  a conference April 4–8\, 2022;  and a workshop from May 2–5\, 2022. \n\n  \n\n\n\n\nSchedule\nSpeaker\nTitle\nAbstract\n\n\nMarch 1 – 3\, 2022\n10:00 am – 12:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nDr. Stefan Czimek\nCharacteristic Gluing for the Einstein Equations\nAbstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface.  Then we turn to bifurcate characteristic gluing (i.e.  gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically\, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).\n\n\nMarch 22 – 25\, 2022\n22nd & 23rd\, 10:00 am – 11:30am ET\n24th & 25th\, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Lan-Hsuan Huang\nExistence of Static Metrics with Prescribed Bartnik Boundary Data\nAbstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold\, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat\, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein\, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts\, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique\, asymptotically flat\, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course\, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An\, and the tentative plan is \n1. The conjecture and an overview of the results\n2. Static regular: a sufficient condition for existence and local uniqueness\n3. Convex boundary\, isometric embedding\, and static regular\n4. Perturbations of any hypersurface are static regular \nVideo on Youtube: March 22\, 2022\n\n\nMarch 29 – April 1\, 2022 10:00am – 12:00pm ET\, each day \nLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Martin Taylor\nThe nonlinear stability of the Schwarzschild family of black holes\nAbstract: I will present aspects of a theorem\, joint with Mihalis Dafermos\, Gustav Holzegel and Igor Rodnianski\, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.\n\n\nApril 19 & 21\, 2022\n10 am – 12 pm ET\, each dayZoom only\nProf. Håkan Andréasson\nTwo topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.\nAbstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole. \nVideo 4/19/2022 \nVideo 4/22/2022\n\n\nMay 16 – 17\, 2022\n10:00 am – 1:00 pm ET\, each dayLocation: Hybrid. CMSA main seminar room\, G-10.\nProf. Marcelo Disconzi\nA brief overview of recent developments in relativistic fluids\nAbstract: In this series of lectures\, we will discuss some recent developments in the field of relativistic fluids\, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary\, a new formulation of the relativistic Euler equations tailored to applications to shock formation\, and formulations of relativistic fluids with viscosity. \n1. Set-up\, review of standard results\, physical motivation.\n2. The relativistic Euler equations: null structures and the problem of shocks.\n3. The free-boundary relativistic Euler equations with a physical vacuum boundary.\n4. Relativistic viscous fluids. \nVideo 5/16/2022 \nVideo 5/17/2022
URL:https://cmsa.fas.harvard.edu/event/grminicourses/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260504T140042
CREATED:20230730T180327Z
LAST-MODIFIED:20240301T070636Z
UID:10001146-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:On renormalisation group induced moduli stabilisation and brane-antibrane inflation
DESCRIPTION:Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-swampland-seminar-series/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260504T140042
CREATED:20240214T082503Z
LAST-MODIFIED:20240301T113123Z
UID:10002586-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:Black Hole Spectroscopy
DESCRIPTION:Abstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220329T090000
DTEND;TZID=America/New_York:20220329T100000
DTSTAMP:20260504T140042
CREATED:20240213T110525Z
LAST-MODIFIED:20240304T102009Z
UID:10002473-1648544400-1648548000@cmsa.fas.harvard.edu
SUMMARY:Combinatorics\, Physics and Probability Seminar
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a seminar on Combinatorics\, Physics and Probability\, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend\, please fill out this form\, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu). \nThe schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/25/2022\n*note special time 9:00–10:00 AM ET\nJacob Bourjaily (Penn State University\, Eberly College of Science\nTitle: Adventures in Perturbation Theory \nAbstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form\, underlying geometric structure\, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress\, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.\n\n\n2/3/2022\nRan Tessler\n(Weizmann Institute of Science)\nTitle: The Amplituhedron BCFW Triangulation \nAbstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells\, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.\n\n\n2/8/2022\nAnna Seigal (Harvard)\nTitle: Invariant theory for maximum likelihood estimation \nAbstract:  I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola\, Kathlén Kohn\, and Philipp Reichenbach.\n\n\n2/15/2022\nIgor Balla\, Hebrew University of Jerusalem\nTitle: Equiangular lines and regular graphs \nAbstract: In 1973\, Lemmens and Seidel asked to determine N_alpha(r)\, the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently\, this problem has been almost completely settled when r is exponentially large relative to 1/alpha\, with the approach both relying on Ramsey’s theorem\, as well as being limited by it. In this talk\, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation\, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular\, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5). \nOur projection method generalizes to complex equiangular lines in C^r\, which may be of independent interest in quantum theory. Applying this method also allows us to obtain\nthe first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha)\, an extension of the Alon-Boppana theorem to dense regular graphs\, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r\, an improvement to Welch’s bound in coding theory.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/21/2021\nNima Arkani-Hamed\nIAS (Institute for Advanced Study)\, School of Natural Sciences\nTitle: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes\n\n\n9/28/2021\nMelissa Sherman-Bennett\nUniversity of Michigan\, Department of Mathematics\nTitle: The hypersimplex and the m=2 amplituhedron \nAbstract: I’ll discuss a curious correspondence between the m=2 amplituhedron\, a 2k-dimensional subset of Gr(k\, k+2)\, and the hypersimplex\, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map\, respectively)\, but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). Along the way\, we prove the sign-flip description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers (inspired by an analogous hypersimplex decomposition).\n\n\n10/5/2021\nDaniel Cizma\, Hebrew University\nTitle: Geodesic Geometry on Graphs \nAbstract: In a graph G = (V\, E) we consider a system of paths S so that for every two vertices u\,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths\, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case\, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w. \nWe’ll discuss the concept of graph metrizability\, and\, in particular\, we’ll see that while metrizability is a rare property\, there exists infinitely many 2-connected metrizable graphs. \nJoint work with Nati Linial.\n\n\n10/12/2021\nLisa Sauermann\, MIT\nTitle: On counting algebraically defined graphs \nAbstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane)\, the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes\, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials)\, and this lower bound essentially matches the upper bound from Warren’s theorem.\n\n\n10/19/2021\nPavel Galashin\nUCLA\, Department of Mathematics\nTitle: Ising model\, total positivity\, and criticality \nAbstract: The Ising model\, introduced in 1920\, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature\, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.\nThe totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases\, and is closely related to cluster algebras and scattering amplitudes.\nI will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian\, obtained in our recent work with P. Pylyavskyy. Building on this connection\, I will give a new boundary correlation formula for the critical Ising model.\n\n\n10/26/2021\nCandida Bowtell\, University of Oxford\nTitle: The n-queens problem \nAbstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash.\n\n\n11/9/2021\nSteven Karp\nUniversite du Quebec a Montreal\, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)\nTitle: Gradient flows on totally nonnegative flag varieties\n\nAbstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic\, geometric\, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications\, we show how the classical Toda flow fits into this framework\, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.\n\n\n11/16/2021\n*note special time 12:30–1:30 ET*\nYinon Spinka (University of British Columbia)\nTitle: A tale of two balloons \nAbstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch\, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law\, and generalize bounds on independent sets that are factors of IID on trees.\nJoint work with Omer Angel and Gourab Ray.\n\n\n11/23/2021\nLutz Warnke (UC San Diego)\nTitle: Prague dimension of random graphs \nAbstract: The Prague dimension of graphs was introduced by Nesetril\, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity\, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor\, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities\, i.e.\, edges of size O(log n).\n\n\n11/30/2021\nKarel Devriendt (University of Oxford)\nTitle: Resistance curvature – a new discrete curvature on graphs \nAbstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals\, for instance by Lin-Lu-Yau\, Forman and Ollivier\, that replicate important curvature theorems and have inspired applications in a variety of practical settings.\nIn this talk\, I will introduce a new notion of discrete curvature on graphs\, which we call the resistance curvature\, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense\, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs\, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.\nFinally\, if time permits I will draw a connection with the geometry of hyperacute simplices\, following the work of Miroslav Fiedler.\nThis work was done in collaboration with Renaud Lambiotte.\n\n\n12/7/2021\nMatthew Jenssen (University of Birmingham)\nTitle: The singularity probability of random symmetric matrices \nAbstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1\,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos\, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.\n\n\n12/14/2021\nStefan Glock (ETH Zurich)\nTitle: The longest induced path in a sparse random graph \nAbstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size\, which seems to be a barrier for certain natural approaches. Recently\, in joint work with Draganic and Krivelevich\, we solved this problem. In the talk\, I will discuss the history of the problem and give an overview of the proof.\n\n\n12/21/2021\n\n\n\n\n01/25/2022\nJacob Bourjaily\nPenn State University\, Department of Physics
URL:https://cmsa.fas.harvard.edu/event/combinatorics-physics-and-probability-seminar/
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DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20260504T140042
CREATED:20240214T035843Z
LAST-MODIFIED:20240502T150948Z
UID:10002518-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Edge Modes and Gravity
DESCRIPTION:Speaker: Rob Leigh\, UIUC \nTitle: Edge Modes and Gravity \nAbstract:  In this talk I first review some of the many appearances of localized degrees of freedom — edge modes —  in a variety of physical systems. Edge modes are implicated for example in quantum entanglement and in various topological and holographic dualities. I then review recent work in which it has been realized that a careful treatment of such modes\, paying attention to relevant symmetries\, is required in order to properly understand such basic physical quantities as Noether charges. From many points of view\, it is conjectured that this physics may be pointing at basic properties of quantum spacetimes and gravity.
URL:https://cmsa.fas.harvard.edu/event/edge-modes-and-gravity/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.30.2022-2.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20260504T140042
CREATED:20240214T080954Z
LAST-MODIFIED:20240301T113038Z
UID:10002582-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Elliptic chiral homology and chiral index
DESCRIPTION:Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application\, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].
URL:https://cmsa.fas.harvard.edu/event/3-29-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220330_Si-LI_poster-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T103000
DTEND;TZID=America/New_York:20220330T120000
DTSTAMP:20260504T140042
CREATED:20240214T103058Z
LAST-MODIFIED:20240301T064220Z
UID:10002673-1648636200-1648641600@cmsa.fas.harvard.edu
SUMMARY:Renormalization group flow as optimal transport
DESCRIPTION:Youtube Video \n  \nAbstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy.  This gives a surprising information-theoretic formulation of the exact renormalization group\, expressed in the language of optimal transport.  We will provide reviews of both the exact renormalization group\, as well as the theory of optimal transportation.  Our results allow us to establish a new\, non-perturbative RG monotone\, and also reformulate RG flow as a variational problem.  The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories.  Our techniques generalize to other RG flow equations beyond Polchinski’s.
URL:https://cmsa.fas.harvard.edu/event/3-30-2022-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.30.2022-1583x2048-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T140000
DTEND;TZID=America/New_York:20220330T150000
DTSTAMP:20260504T140042
CREATED:20230808T183529Z
LAST-MODIFIED:20240515T202223Z
UID:10001209-1648648800-1648652400@cmsa.fas.harvard.edu
SUMMARY:Memorizing Transformers
DESCRIPTION:Speaker: Yuhuai Wu\, Stanford and Google \nTitle: Memorizing Transformers \nAbstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge\, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time\, thus acquiring new knowledge immediately. In this talk\, I will discuss how we extend language models with the ability to memorize the internal representations of past inputs. We demonstrate that an approximate NN lookup into a non-differentiable memory of recent (key\, value) pairs improves language modeling across various benchmarks and tasks\, including generic webtext (C4)\, math papers (arXiv)\, books (PG-19)\, code (Github)\, as well as formal theorems (Isabelle). We show that the performance steadily improves when we increase the size of memory up to 262K tokens. We also find that the model is capable of making use of newly defined functions and theorems during test time.
URL:https://cmsa.fas.harvard.edu/event/3-30-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.30.2022-1583x2048-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220331T152000
DTEND;TZID=America/New_York:20220331T172000
DTSTAMP:20260504T140042
CREATED:20240214T113726Z
LAST-MODIFIED:20240301T103621Z
UID:10002704-1648740000-1648747200@cmsa.fas.harvard.edu
SUMMARY:Compactification of an embedded vector space and its combinatorics
DESCRIPTION:Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space.  Many fundamental questions have been open for these classical objects.  We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry.  Key objects involve compactifications of embedded vector spaces\, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector bundles and the cohomology ring of stellahedral varieties.
URL:https://cmsa.fas.harvard.edu/event/3-31-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.231.2022-1583x2048-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220401T090000
DTEND;TZID=America/New_York:20220401T103000
DTSTAMP:20260504T140042
CREATED:20240214T084536Z
LAST-MODIFIED:20240301T110938Z
UID:10002596-1648803600-1648809000@cmsa.fas.harvard.edu
SUMMARY:Diffusive growth sourced by topological defects
DESCRIPTION:Member Seminar \nSpeaker: Farzan Vafa \nTitle: Diffusive growth sourced by topological defects \nAbstract: In this talk\, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time\, and predict that in the presence of a positive defect\, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature\, we exploit the fact that for axisymmetric surfaces\, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry\, for polar order and small bending modulus\, is a deformed football.\nWe apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells\, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting\, we show that the defect configuration consisting of a bound +1 defect state\, which is stabilized by activity\, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles\, consistent with observations of a basal marine invertebrate Hydra
URL:https://cmsa.fas.harvard.edu/event/4-1-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T093000
DTEND;TZID=America/New_York:20220408T170000
DTSTAMP:20260504T140042
CREATED:20230705T082708Z
LAST-MODIFIED:20250305T172217Z
UID:10000087-1649064600-1649437200@cmsa.fas.harvard.edu
SUMMARY:General Relativity Conference
DESCRIPTION:Schedule | April 4–8\, 2022\nMonday\, April 4\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPieter Blue\, University of Edinburgh\, UK\n(virtual)\nTitle: Linear stability of the Kerr spacetime in the outgoing radiation gauge \nAbstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation\, the linearisation of the Einstein equation in this gauge\, and the decay of solutions to the linearised Einstein equation around Kerr black holes in this gauge. The stability of the family of Kerr black holes under the evolution generated by the Einstein equation is a long-standing problem in mathematical relativity. In 1972\, Teukolsky discovered equations governing certain components of the linearised curvature that are invariant under linearised gague transformations. In 1975\, Chrzanowski introduced the “outgoing radiation gauge”\, a condition on the linearised metric that allows for the construction of the linearised metric from the linearised curvature. In 2019\, we proved decay for the metric constructed using Chrzanowski’s outgoing radiation gauge. Recently\, using a flow along null geodesics\, we have constructed a new gauge such that\, in this gauge\, the Einstein equation is well posed and such that the linearisation is Chrzanowski’s outgoing radiation gauge. \nThis is joint work with Lars Andersson\, Thomas Backdahl\, and Siyuan Ma.\n\n\n10:30 am–11:30 am\nPeter Hintz\, ETH Zürich\n(virtual)\nTitle: Mode stability and shallow quasinormal modes of Kerr-de Sitter\nblack holesAbstract: The Kerr-de Sitter metric describes a rotating black hole with mass $m$ and specific angular momentum $a$ in a universe\, such as our own\, with cosmological constant $\Lambda>0$. I will explain a proof of mode stability for the scalar wave equation on Kerr-de Sitter spacetimes in the following setting: fixing $\Lambda$ and the ratio $|a/m|<1$ (related to the subextremality of the black hole in question)\, mode stability holds for sufficiently small black hole mass $m$. We also obtain estimates for the location of quasinormal modes (resonances) $\sigma$ in any fixed half space $\Im\sigma>-C$. Our results imply that solutions of the wave equation decay exponentially in time to constants\, with an explicit exponential rate. The proof is based on careful uniform estimates for the spectral family in the singular limit $m\to 0$ in which\, depending on the scaling\, the Kerr-de Sitter spacetime limits to a Kerr or the de Sitter spacetime.\n\n\n11:30 am–12:30 pm\nLars Andersson\, Albert Einstein Institute\, Germany\n(virtual)\nTitle: Gravitational instantons and special geometry \nAbstract: Gravitational instantons are Ricci flat complete Riemannian 4-manifolds with at least quadratic curvature decay. In this talk\, I will introduce some notions of special geometry\, discuss known examples\, and mention some open questions. The Chen-Teo gravitational instanton is an asymptotically flat\, toric\, Ricci flat family of metrics on $\mathrm{CP}^2 \setminus \mathrm{S}^1$\, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. I will sketch a proof that the Chen-Teo Instanton is Hermitian and non-Kähler. Thus\, all known examples of gravitational instantons are Hermitian. This talks is based on joint work with Steffen Aksteiner\, cf. https://arxiv.org/abs/2112.11863.\n\n\n12:30 pm–1:30 pm\nbreak\n\n\n\n1:30 pm–2:30 pm\nMartin Taylor\, Imperial College London\n(virtual)\nTitle: The nonlinear stability of the Schwarzschild family of black holes \nAbstract: I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge\, is expressed entirely in physical space\, and utilises the analysis of Dafermos–Holzegel–Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos\, G. Holzegel and I. Rodnianski.\n\n\n2:30 pm–3:30 pm\nPo-Ning Chen\, University of California\, Riverside\n(virtual)\nTitle: Angular momentum in general relativity\n\nAbstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960s\, due to the ‘supertranslation ambiguity’. In this talk\, we will discuss how the mathematical theory of quasilocal mass and angular momentum leads to a new definition of angular momentum at null infinity that is free of any supertranslation ambiguity.This is based on joint work with Jordan Keller\, Mu-Tao Wang\, Ye-Kai Wang\, and Shing-Tung Yau.\n\n\n3:30 pm–4:00 pm\nbreak\n\n\n\n4:00 pm–5:00 pm\nDan Lee\, Queens College (CUNY)\n(hybrid: in person & virtual)\nTitle: Stability of the positive mass theorem \nAbstract: We will discuss the problem of stability for the rigidity part of the Riemannian positive mass theorem\, focusing on recent work with Kazaras and Khuri\, in which we proved that if one assumes a lower Ricci curvature bound\, then stability holds with respect to pointed Gromov-Hausdorff convergence.\n\n\n\n\n  \nTuesday\, April 5\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nXinliang An\, National University of Singapore\n(virtual)\nTitle: Anisotropic dynamical horizons arising in gravitational collapse \nAbstract: Black holes are predicted by Einstein’s theory of general relativity\, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being and about the structures of their inner spacetime singularities. In this talk\, we will present several results in these directions. First\, in a joint work with Qing Han\, with tools from scale-critical hyperbolic method and non-perturbative elliptic techniques\, with anisotropic characteristic initial data we prove that: in the process of gravitational collapse\, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This result extends the 2008 Christodoulou’s monumental work and it connects to black hole thermodynamics along the apparent horizon. Second\, in joint works with Dejan Gajic and Ruixiang Zhang\, for the spherically symmetric Einstein-scalar field system\, we derive precise blow-up rates for various geometric quantities along the inner spacelike singularities. These rates obey polynomial blow-up upper bounds; and when it is close to timelike infinity\, these rates are not limited to discrete finite choices and they are related to the Price’s law along the event horizon. This indicates a new blow-up phenomenon\, driven by a PDE mechanism\, rather than an ODE mechanism. If time permits\, some results on fluid dynamics will also be addressed.\n\n\n10:30 am–11:30 am\nSergiu Klainerman\, Princeton\n(virtual)\nTitle: Nonlinear stability of slowly rotating Kerr solutions \nAbstract: I will talk about the status of the stability of Kerr conjecture in General Relativity based on recent results obtained in collaboration with Jeremie Szeftel and Elena Giorgi.\n\n\n11:30 am–12:30 pm\nSiyuan Ma\, Sorbonne University\n(virtual)\nTitle: Sharp decay for Teukolsky master equation \nAbstract: I will talk about joint work with L. Zhang on deriving the late time dynamics of the spin $s$ components that satisfy the Teukolsky master equation in Kerr spacetimes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJonathan Luk\, Stanford\n(virtual)\nTitle: A tale of two tails \nAbstract: Motivated by the strong cosmic censorship conjecture\, we introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes in odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results\, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover\, we show that the late-time tails are in general different from the stationary case in the presence of dynamical and/or nonlinear perturbations. This is a joint work with Sung-Jin Oh (Berkeley).\n\n\n2:30 pm–3:30 pm\nGary Horowitz\, University of California Santa Barbara\n(virtual)\nTitle: A new type of extremal black hole \nAbstract: I describe a family of four-dimensional\, asymptotically flat\, charged black holes that develop (charged) scalar hair as one increases their charge at fixed mass. Surprisingly\, the maximum charge for given mass is a nonsingular hairy black hole with a nondegenerate event horizon. Since the surface gravity is nonzero\, if quantum matter is added\, Hawking radiation does not appear to stop when this new extremal limit is reached. This raises the question of whether Hawking radiation will cause the black hole to turn into a naked singularity. I will argue that does not occur.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nLydia Bieri\, University of Michigan\n(virtual)\nTitle: Gravitational radiation in general spacetimes \nAbstract: Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers\, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk\, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set\, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular\, whereas the former sources produce memory effects that are finite and of purely electric parity\, the latter in addition generate memory of magnetic type\, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.\n\n\n\n\n  \nWednesday\, April 6\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nGerhard Huisken\, Mathematisches Forschungsinstitut Oberwolfach\n(virtual)\nTitle: Space-time versions of inverse mean curvature flow \nAbstract: In order to extend the Penrose inequality from a time-symmetric setting to general asymptotically flat initial data sets several anisotropic generalisations of inverse mean curvature flow have been suggested that take the full space-time geometry into account. The lecture describes the properties of such flows and reports on recent joint work with Markus Wolff on inverse flow along the space-time mean curvature.\n\n\n10:30 am–11:30 am\nCarla Cederbaum\, Universität Tübingen\, Germany\n(virtual)\nTitle: Coordinates are messy \nAbstract: Asymptotically Euclidean initial data sets $(M\,g\,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast\, respectively. Provided their matter densities satisfy suitable integrability conditions\, they have well-defined (ADM-)energy\, (ADM-)linear momentum\, and (ADM-)mass. This was proven by Bartnik using harmonic coordinates. To study their (ADM-)angular momentum and (BORT-)center of mass\, one usually assumes the existence of Regge—Teitelboim coordinates on the initial data set $(M\,g\,K)$ in question. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates We will also show that harmonic coordinates can be used as a tool in checking whether a given asymptotically Euclidean initial data set possesses Regge—Teitelboim coordinates. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences these findings have for the definition of the center of mass\, relying on joint work with Nerz and with Sakovich.\n\n\n11:30 am–12:30 pm\nStefanos Aretakis\, University of Toronto\n(virtual)\nTitle: Observational signatures for extremal black holes \nAbstract: We will present results regarding the asymptotics of scalar perturbations on black hole backgrounds. We will then derive observational signatures for extremal black holes that are based on global or localized measurements on null infinity. This is based on joint work with Gajic-Angelopoulos and ongoing work with Khanna-Sabharwal.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nJared Speck\, Vanderbilt University\n(virtual)\nTitle: The mathematical theory of shock waves in multi-dimensional relativistic and non-relativistic compressible Euler flow \nAbstract: In the last two decades\, there have been dramatic advances in the rigorous mathematical theory of shock waves in solutions to the relativistic Euler equations and their non-relativistic analog\, the compressible Euler equations. A lot of the progress has relied on techniques that were developed to study Einstein’s equations. In this talk\, I will provide an overview of the field and highlight some recent progress on problems without symmetry or irrotationality assumptions. I will focus on results that reveal various aspects of the structure of the maximal development of the data and the corresponding implications for the shock development problem\, which is the problem of continuing the solution weakly after a shock. I will also describe various open problems\, some of which are tied to the Einstein–Euler equations. Various aspects of this program are joint with L. Abbrescia\, M. Disconzi\, and J. Luk.\n\n\n2:30 pm–3:30 pm\nLan-Hsuan Huang\, University of Connecticut\n(virtual)\nTitle: Null perfect fluids\, improvability of dominant energy scalar\, and Bartnik mass minimizers \nAbstract: We introduce the concept of improvability of the dominant energy scalar\, and we derive strong consequences of non-improvability. In particular\, we prove that a non-improvable initial data set without local symmetries must sit inside a null perfect fluid spacetime carrying a global Killing vector field. We also show that the dominant energy scalar is always almost improvable in a precise sense. Using these main results\, we provide a characterization of Bartnik mass minimizing initial data sets which makes substantial progress toward Bartnik’s stationary conjecture. \nAlong the way we observe that in dimensions greater than eight there exist pp-wave counterexamples (without the optimal decay rate for asymptotically flatness) to the equality case of the spacetime positive mass theorem. As a consequence\, we find counterexamples to Bartnik’s stationary and strict positivity conjectures in those dimensions. This talk is based on joint work with Dan A. Lee.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nDemetre Kazaras\, Duke University\n(virtual)\nTitle: Comparison geometry for scalar curvature and spacetime harmonic functions \nAbstract: Comparison theorems are the basis for our geometric understanding of Riemannian manifolds satisfying a given curvature condition. A remarkable example is the Gromov-Lawson toric band inequality\, which bounds the distance between the two sides of a Riemannian torus-cross-interval with positive scalar curvature by a sharp constant inversely proportional to the scalar curvature’s minimum. We will give a new qualitative version of this and similar band-type inequalities in dimension 3 using the notion of spacetime harmonic functions\, which recently played the lead role in our recent proof of the positive mass theorem. This is joint work with Sven Hirsch\, Marcus Khuri\, and Yiyue Zhang.\n\n\n\n\n  \nThursday\, April 7\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nPiotr Chrusciel\, Universitat Wien\n(virtual)\nTitle: Maskit gluing and hyperbolic mass \nAbstract: “Maskit gluing” is a gluing construction for asymptotically locally hyperbolic (ALH) manifolds with negative cosmological constant. I will present a formula for the mass of Maskit-glued ALH manifolds and describe how it can be used to construct general relativistic initial data with negative mass.\n\n\n10:30 am–11:30 am\nGreg Galloway\, University of Miami (virtual)\nTitle:  Initial data rigidity and applications \nAbstract:  We present a result from our work with Michael Eichmair and Abraão Mendes concerning initial data rigidity results (CMP\, 2021)\, and look at some consequences.  In a note with Piotr Chruściel (CQG 2021)\, we showed how to use this result\, together with arguments from Chruściel and Delay’s proof of the their hyperbolic PMT result\, to obtain a hyperbolic PMT result with boundary.  This will also be discussed.\n\n\n11:30 am–12:30 pm\nPengzi Miao\, University of Miami\n(virtual)\nTitle: Some remarks on mass and quasi-local mass \nAbstract: In the first part of this talk\, I will describe how to detect the mass of asymptotically flat and asymptotically hyperbolic manifolds via large Riemannian polyhedra. In the second part\, I will discuss an estimate of the Bartnik quasi-local mass and its geometric implications. This talk is based on several joint works with A. Piubello\, and with H.C. Jang.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nYakov Shlapentokh Rothman\, Princeton\n(hybrid: in person & virtual)\nTitle: Self-Similarity and Naked Singularities for the Einstein Vacuum Equations \nAbstract: We will start with an introduction to the problem of constructing naked singularities for the Einstein vacuum equations\, and then explain our discovery of a fundamentally new type of self-similarity and show how this allows us to construct solutions corresponding to a naked singularity. This is joint work with Igor Rodnianski.\n\n\n2:30 pm–3:30 pm\nMarcelo Disconzi\, Vanderbilt University\n(virtual)\nTitle: General-relativistic viscous fluids. \nAbstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions\, as the quark-gluon plasma is the hottest\, smallest\, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe\, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades\, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments\, theory\, phenomenology\, and numerical simulations. From these investigations\, a coherent picture has emerged\, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently\, state-of-the-art numerical simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems\, a robust and mathematically sound theory of relativistic fluids with viscosity is still lacking. This is due\, in part\, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk\, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nMaxime van de Moortel\, Princeton\n(hybrid: in person & virtual)\nTitle: Black holes: the inside story of gravitational collapse \nAbstract: What is inside a dynamical black hole? While the local region near time-like infinity is understood for various models\, the global structure of the black hole interior has largely remained unexplored.\nThese questions are deeply connected to the nature of singularities in General Relativity and celebrated problems such as Penrose’s Strong Cosmic Censorship Conjecture.\nI will present my recent resolution of these problems in spherical gravitational collapse\, based on the discovery of a novel phenomenon: the breakdown of weak singularities and the dynamical formation of a strong singularity.\n\n\n\n\n  \nFriday\, April 8\, 2022 \n\n\n\n\nTime (ET)\nSpeaker\nTitle/Abstract\n\n\n9:30 am–10:30 am\nYe-Kai Wang\, National Cheng Kun University\, Taiwan\n(virtual)\nTitle: Supertranslation invariance of angular momentum at null infinity in double null gauge \nAbstract: This talk accompanies Po-Ning Chen’s talk on Monday with the results described in the double null gauge rather than Bondi-Sachs coordinates. Besides discussing\nhow Chen-Wang-Yau angular momentum resolves the supertranslation ambiguity\, we also review the definition of angular momentum defined by A. Rizzi. The talk is based on the joint work with Po-Ning Chen\, Jordan Keller\, Mu-Tao Wang\, and Shing-Tung Yau.\n\n\n10:30 am–11:30 am\nZoe Wyatt\, King’s College London\n(virtual)\nTitle: Global Stability of Spacetimes with Supersymmetric Compactifications \nAbstract: Spacetimes with compact directions which have special holonomy\, such as Calabi-Yau spaces\, play an important role in\nsupergravity and string theory. In this talk I will discuss a recent work with Lars Andersson\, Pieter Blue and Shing-Tung Yau\, where we show the global\, nonlinear stability a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. This stability result is related to a conjecture of Penrose concerning the validity of string theory. Our proof uses the intersection of methods for quasilinear wave and Klein-Gordon equations\, and so towards the end of the talk I will also comment more generally on coupled wave–Klein-Gordon equations.\n\n\n11:30 am–12:30 pm\nElena Giorgi\, Columbia University\n(hybrid: in person & virtual)\nTitle: The stability of charged black holes \nAbstract: Black hole solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.\n\n\n12:30 pm–1:30 pm\nBreak\n\n\n\n1:30 pm–2:30 pm\nMarcus Khuri\, Stony Brook University\n(virtual)\nTitle: The mass-angular momentum inequality for multiple black holes\n\nAbstract: Consider a complete 3-dimensional initial data set for the Einstein equations which has multiple asymptotically flat or asymptotically cylindrical ends. If it is simply connected\, axisymmetric\, maximal\, and satisfies the appropriate energy condition then the ADM mass of any of the asymptotically flat ends is bounded below by the square root of the total angular momentum. This generalizes previous work of Dain\, Chrusciel-Li-Weinstein\, and Schoen-Zhou which treated either the single black hole case or the multiple black hole case without an explicit lower bound. The proof relies on an analysis of the asymptotics of singular harmonic maps from\nR^3 \ \Gamma –>H^2   where \Gamma is a coordinate axis. This is joint work with Q. Han\, G. Weinstein\, and J. Xiong.\n\n\n2:30 pm–3:30 pm\nMartin Lesourd\, Harvard\n(hybrid: in person & virtual)\nTitle:  A Snippet on Mass and the Topology and Geometry of Positive Scalar Curvature \nAbstract:  I will talk about a small corner of the study of Positive Scalar Curvature (PSC) and questions which are most closely related to the Positive Mass Theorem. The classic questions are ”which topologies allow for PSC?” and ”what is the geometry of manifolds with PSC?”. This is based on joint work with Prof. S-T. Yau\, Prof. D. A. Lee\, and R. Unger.\n\n\n3:30 pm–4:00 pm\nBreak\n\n\n\n4:00 pm–5:00 pm\nGeorgios Moschidis\, Princeton\n(virtual)\nTitle: Weak turbulence for the Einstein–scalar field system. \nAbstract: In the presence of confinement\, the Einstein field equations are expected to exhibit turbulent dynamics. In the presence of a negative cosmological constant\, the AdS instability conjecture claims the existence of arbitrarily small perturbations to the initial data of Anti-de Sitter spacetime which\, under evolution by the vacuum Einstein equations with reflecting boundary conditions at conformal infinity\, lead to the formation of black holes after sufficiently long time.\nIn this talk\, I will present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein-scalar field system. The construction of the unstable initial data will require carefully designing a family of initial configurations of localized matter beams and estimating the exchange of energy taking place between interacting beams over long periods of time\, as well as estimating the decoherence rate of those beams.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-conference/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/GR-Conference.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T100000
DTEND;TZID=America/New_York:20220404T230000
DTSTAMP:20260504T140042
CREATED:20230730T180720Z
LAST-MODIFIED:20240301T073634Z
UID:10001147-1649066400-1649113200@cmsa.fas.harvard.edu
SUMMARY:Causality constraints on corrections to Einstein gravity
DESCRIPTION:Swampland Seminar \nSpeakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech) \n\n\nTitle: Causality constraints on corrections to Einstein gravity \n\nAbstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together\, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations\, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0\, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality\, together with the non-observation of gravitationally-coupled higher-spin states at colliders\, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.
URL:https://cmsa.fas.harvard.edu/event/4-5-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220404T190000
DTEND;TZID=America/New_York:20220404T200000
DTSTAMP:20260504T140042
CREATED:20230705T082949Z
LAST-MODIFIED:20250328T200243Z
UID:10000085-1649098800-1649102400@cmsa.fas.harvard.edu
SUMMARY:Second Annual Yip Lecture: Extraterrestrial Life
DESCRIPTION:Harvard CMSA hosted the second annual Yip Lecture on April 4\, 2022. \nThe Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.\nThis year’s speaker was Avi Loeb (Harvard). \n  \n \nExtraterrestrial Life\nAbstract: Are we alone? It would be arrogant to think that we are\, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres\, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”\, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System\, such as `Oumuamua. \n\nAbraham (Avi) Loeb is the Frank B. Baird\, Jr.\, Professor of Science at Harvard University and a bestselling author (in lists of the New York Times\, Wall Street Journal\, Publishers Weekly\, Die Zeit\, Der Spiegel\, L’Express and more). He received a PhD in Physics from the Hebrew University of Jerusalem in Israel at age 24 (1980–1986)\, led the first international project supported by the Strategic Defense Initiative (1983–1988)\, and was subsequently a long-term member of the Institute for Advanced Study at Princeton (1988–1993). Loeb has written 8 books\, including most recently\, Extraterrestrial (Houghton Mifflin Harcourt\, 2021)\, and nearly a thousand papers (with an h-index of 118) on a wide range of topics\, including black holes\, the first stars\, the search for extraterrestrial life\, and the future of the Universe. Loeb is the head of the Galileo Project in search for extraterrestrial intelligence\, the Director of the Institute for Theory and Computation (2007–present) within the Harvard-Smithsonian Center for Astrophysics\, and also serves as the Head of the Galileo Project (2021–present). He had been the longest serving Chair of Harvard’s Department of Astronomy (2011–2020) and the Founding Director of Harvard’s Black Hole Initiative (2016–2021). He is an elected fellow of the American Academy of Arts & Sciences\, the American Physical Society\, and the International Academy of Astronautics. Loeb is a former member of the President’s Council of Advisors on Science and Technology (PCAST) at the White House\, a former chair of the Board on Physics and Astronomy of the National Academies (2018–2021) and a current member of the Advisory Board for “Einstein: Visualize the Impossible” of the Hebrew University. He also chairs the Advisory Committee for the Breakthrough Starshot Initiative (2016–present) and serves as the Science Theory Director for all Initiatives of the Breakthrough Prize Foundation. In 2012\, TIME magazine selected Loeb as one of the 25 most influential people in space and in 2020 Loeb was selected among the 14 most inspiring Israelis of the last decade. \nClick here for Loeb’s commentaries on innovation and diversity. \nWebsite: https://www.cfa.harvard.edu/~loeb/ \nSee the Harvard Gazette article featuring Avi Loeb: “Oh\, if I could talk to the aliens” published March 8\, 2022. \nProf. Loeb’s books:\nExtraterrestrial: The First Sign of Intelligent Life Beyond Earth (2021)\nLife in the Cosmos: From Biosignatures to Technosignatures (2021) \nAvil Loeb is the head of the Galileo Project at Harvard. \n\nThe previous Yip Lecture featured Peter Galison (Harvard)\, who spoke on the EHT’s hunt for an objective image of a black hole.
URL:https://cmsa.fas.harvard.edu/event/second-annual-yip-lecture/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Public Lecture,Special Lectures,Yip Lecture Series
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Yip2022_poster_web.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220405T093000
DTEND;TZID=America/New_York:20220405T103000
DTSTAMP:20260504T140042
CREATED:20230825T075918Z
LAST-MODIFIED:20240304T082856Z
UID:10001293-1649151000-1649154600@cmsa.fas.harvard.edu
SUMMARY:Regularized integrals on Riemann surfaces and correlations functions in 2d chiral CFTs
DESCRIPTION:Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces\, introduced by Si Li and myself in arXiv:2008.07503\, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs\, holomorphic anomaly equations\, etc. If time permits\, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures. \nThe talk is partially based on joint works with Si Li.
URL:https://cmsa.fas.harvard.edu/event/regularized-integrals-on-riemann-surfaces-and-correlations-functions-in-2d-chiral-cfts/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.05.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T093000
DTEND;TZID=America/New_York:20220406T103000
DTSTAMP:20260504T140042
CREATED:20240214T035619Z
LAST-MODIFIED:20240304T073658Z
UID:10002517-1649237400-1649241000@cmsa.fas.harvard.edu
SUMMARY:What is Mathematical Consciousness Science?
DESCRIPTION:Speaker: Johannes Kleiner\, LMU München \nTitle: What is Mathematical Consciousness Science? \nAbstract: In the last three decades\, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists\, psychologists\, and philosophers. Recently\, a decidedly mathematical perspective has emerged as well\, which is now called Mathematical Consciousness Science. In this talk\, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians\, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.
URL:https://cmsa.fas.harvard.edu/event/what-is-mathematical-consciousness-science/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-04.06.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T103000
DTEND;TZID=America/New_York:20220406T120000
DTSTAMP:20260504T140042
CREATED:20240214T102826Z
LAST-MODIFIED:20240301T064048Z
UID:10002671-1649241000-1649246400@cmsa.fas.harvard.edu
SUMMARY:Late time von Neumann entropy and measurement-induced phase transition
DESCRIPTION:Youtube Video \n  \nAbstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution\, we show that the correlations between different replicas account for the Page curve at late time\, and a permutation group structure emerges in the large-N calculation. In the presence of measurements\, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken\, which shows that the transition occurs at the point of replica symmetry breaking.
URL:https://cmsa.fas.harvard.edu/event/4-6-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-04.06.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T133000
DTEND;TZID=America/New_York:20220406T143000
DTSTAMP:20260504T140042
CREATED:20230801T182005Z
LAST-MODIFIED:20240228T114223Z
UID:10001163-1649251800-1649255400@cmsa.fas.harvard.edu
SUMMARY:On the wave turbulence theory for a stochastic KdV type equation
DESCRIPTION:Random Matrix & Probability Theory Seminar\n\nSpeaker: Minh-Binh TRAN (SMU & MIT)\n\n\n\n\n\nLocation: CMSA\, Room G02 \nTitle: On the wave turbulence theory for a stochastic KdV type equation \nAbstract: We report recent progress\, in collaboration with Gigliola Staffilani (MIT)\, on the problem of deriving kinetic equations from dispersive equations. To be more precise\, starting from the stochastic  Zakharov-Kuznetsov equation\, a multidimensional KdV type equation on a hypercubic lattice\, we provide a derivation of the 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave  kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium\, the dimension is  $d\ge 2$\, the smallness of the nonlinearity $\lambda$ is allowed to be independent of the size of the lattice\, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation.  Unlike the cubic nonlinear Schrodinger equation\, for which such a general result is commonly expected without the noise\, the kinetic description of the deterministic lattice ZK equation is unlikely to happen. One of the key reasons is that the dispersion relation of the lattice ZK equation leads to a singular manifold\, on which not only 3-wave interactions but also all m-wave interactions are allowed to happen. This phenomenon has been first observed by Lukkarinen  as a counterexample for which one of the main tools to derive kinetic equations from wave equations (the suppression of crossings) fails to hold true.
URL:https://cmsa.fas.harvard.edu/event/random_4622/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220406T213000
DTEND;TZID=America/New_York:20220406T223000
DTSTAMP:20260504T140042
CREATED:20240214T080706Z
LAST-MODIFIED:20240301T112919Z
UID:10002581-1649280600-1649284200@cmsa.fas.harvard.edu
SUMMARY:Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds
DESCRIPTION:Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk\, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces\, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type\, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.
URL:https://cmsa.fas.harvard.edu/event/4-5-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
LOCATION:Virtual
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220406_Yalong-CAO_poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T093000
DTEND;TZID=America/New_York:20220407T110000
DTSTAMP:20260504T140042
CREATED:20240214T102601Z
LAST-MODIFIED:20240301T063834Z
UID:10002669-1649323800-1649329200@cmsa.fas.harvard.edu
SUMMARY:Lattice Gauge Theory View of Toric Codes\, X-cube\, and More
DESCRIPTION:Youtube Video \n  \nAbstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability\, it turns out\, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions\, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore\, the transformation properties of the gauge fields in the respective LGT is responsible for\, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are\, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC\, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding. \nReferences:\n[1] “Model for fractions\, fluxons\, and free verte excitations”\, JT Kim\, JH Han\, Phys. Rev. B 104\, 115128 (2021)\n[1] “Rank-2 toric code in two dimensions”\, YT Oh\, JT Kim\, EG Moon\, JH Han\, Phys. Rev. B 105\, 045128 (2022)\n[2] “Effective field theory for the exactly solvable stabilizer spin models”\, JT Kim\, YT Oh\, JH Han\, in preparation.\n[3] “Effective field theory of dipolar braiding statistics in two dimensions”\, YT Oh\, JT Kim\, JH Han\, in preparation.
URL:https://cmsa.fas.harvard.edu/event/4-7-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-04.07.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T130000
DTEND;TZID=America/New_York:20220407T142600
DTSTAMP:20260504T140042
CREATED:20230824T173606Z
LAST-MODIFIED:20240304T082508Z
UID:10001310-1649336400-1649341560@cmsa.fas.harvard.edu
SUMMARY:Theories of branching morphogenesis
DESCRIPTION:Abstract:  The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions\, it remains unclear how macroscopic features of branched organs\, including their size\, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney\, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model\, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then\, based on reconstructions of the developing mouse salivary gland\, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.
URL:https://cmsa.fas.harvard.edu/event/theories-of-branching-morphogenesis/
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-04.07.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T152200
DTEND;TZID=America/New_York:20220407T172200
DTSTAMP:20260504T140042
CREATED:20240214T113556Z
LAST-MODIFIED:20240301T103440Z
UID:10002702-1649344920-1649352120@cmsa.fas.harvard.edu
SUMMARY:The space of vector bundles on spheres: algebra\, geometry\, topology
DESCRIPTION:Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist\, so I will try to explain an algebraic or geometric incarnation\, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory\, and (for the most part) accessible to those in all fields\, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson\, as well as joint work with (separately) Larson and Jim Bryan.
URL:https://cmsa.fas.harvard.edu/event/4-7-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220408T084500
DTEND;TZID=America/New_York:20220408T101500
DTSTAMP:20260504T140042
CREATED:20240214T084325Z
LAST-MODIFIED:20240301T105121Z
UID:10002595-1649407500-1649412900@cmsa.fas.harvard.edu
SUMMARY:Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
DESCRIPTION:Speaker: Jörn Boehnke \nTitle: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning \nAbstract:  In the standard regression discontinuity setting\, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage\, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage\, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score\, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations\, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally\, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
URL:https://cmsa.fas.harvard.edu/event/4-8-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220411T100000
DTEND;TZID=America/New_York:20220411T110000
DTSTAMP:20260504T140042
CREATED:20230730T181035Z
LAST-MODIFIED:20240301T072853Z
UID:10001148-1649671200-1649674800@cmsa.fas.harvard.edu
SUMMARY:Type IIB flux compactifications with $h^{1\,1}=0$
DESCRIPTION:Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions\, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.
URL:https://cmsa.fas.harvard.edu/event/4-11-2021-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220412T093000
DTEND;TZID=America/New_York:20220412T103000
DTSTAMP:20260504T140042
CREATED:20240214T065956Z
LAST-MODIFIED:20240304T060444Z
UID:10002553-1649755800-1649759400@cmsa.fas.harvard.edu
SUMMARY:BCFW recursion relations and non-planar positive geometry
DESCRIPTION:Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk\, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-12-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220412T115800
DTEND;TZID=America/New_York:20220412T125800
DTSTAMP:20260504T140042
CREATED:20230825T080118Z
LAST-MODIFIED:20240304T061648Z
UID:10001294-1649764680-1649768280@cmsa.fas.harvard.edu
SUMMARY:Applications of Higher Determinant Map
DESCRIPTION:Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.
URL:https://cmsa.fas.harvard.edu/event/applications-of-higher-determinant-map/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T093000
DTEND;TZID=America/New_York:20220413T103000
DTSTAMP:20260504T140042
CREATED:20240214T035353Z
LAST-MODIFIED:20240304T073600Z
UID:10002516-1649842200-1649845800@cmsa.fas.harvard.edu
SUMMARY:Quantisation in monoidal categories and quantum operads
DESCRIPTION:Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S\, compatible with this structure. But in fact\, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops\, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics\, in a very definite sense\, going back at least to Archimedes. When quantum physics started to replace classical\, it turned out that classical symmetries must also be replaced by their quantum versions\, e.g. quantum groups. \nIn this talk we explain how to define and study quantum versions of symmetries\, relevant to information theory and other contexts.
URL:https://cmsa.fas.harvard.edu/event/quantisation-in-monoidal-categories-and-quantum-operads/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.13.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T203000
DTEND;TZID=America/New_York:20220413T220000
DTSTAMP:20260504T140042
CREATED:20240214T102340Z
LAST-MODIFIED:20240301T063645Z
UID:10002668-1649881800-1649887200@cmsa.fas.harvard.edu
SUMMARY:Why is the mission impossible? Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
DESCRIPTION:Youtube Video \nAbstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However\, in the related formulation including the mirror Ginsparg-Wilson fermions\, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field\, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase. \nWe re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions\, but a slight modification without such singularity is allowed by virtue of the very nature. \nWe then consider a simpler four-flavor axial gauge model\, the 14(-1)4 model\, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms\, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit\, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior. \nFinally\, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model\, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
URL:https://cmsa.fas.harvard.edu/event/4-13-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.13.22-1583x2048-1.jpg
END:VEVENT
END:VCALENDAR