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DTSTART;TZID=America/New_York:20210913T090000
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DTSTAMP:20260412T052117
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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
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DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260412T052117
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:20260412T052117
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:20260412T052117
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:20220404T093000
DTEND;TZID=America/New_York:20220408T170000
DTSTAMP:20260412T052117
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T093000
DTEND;TZID=America/New_York:20220407T110000
DTSTAMP:20260412T052117
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T130000
DTEND;TZID=America/New_York:20220407T142600
DTSTAMP:20260412T052117
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T152200
DTEND;TZID=America/New_York:20220407T172200
DTSTAMP:20260412T052117
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
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