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DTSTART;TZID=America/New_York:20210913T090000
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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
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DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260411T111714
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:20260411T111714
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:20260411T111714
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:20220506T100000
DTEND;TZID=America/New_York:20220508T170000
DTSTAMP:20260411T111714
CREATED:20230706T181343Z
LAST-MODIFIED:20231227T080733Z
UID:10000104-1651831200-1652029200@cmsa.fas.harvard.edu
SUMMARY:2022 NSF FRG Workshop on Discrete Shapes
DESCRIPTION:On May 6–8\, 2022\, the CMSA  hosted a second NSF FRG Workshop. \nThis project brings together a community of researchers who develop theoretical and computational models to characterize shapes. Their combined interests span Mathematics (Geometry and Topology)\, Computer Science (Scientific Computing and Complexity Theory)\, and domain sciences\, from Data Sciences to Computational Biology. \nScientific research benefits from the development of an ever-growing number of sensors that are able to capture details of the world at increasingly fine resolutions. The seemingly unlimited breadth and depth of these sources provide the means to study complex systems in a more comprehensive way. At the same time\, however\, these sensors are generating a huge amount of data that comes with a high level of complexity and heterogeneity\, providing indirect measurements of hidden processes that provide keys to the systems under study. This has led to new challenges and opportunities in data analysis. Our focus is on image data and the shapes they represent. Advances in geometry and topology have led to powerful new tools that can be applied to geometric methods for representing\, searching\, simulating\, analyzing\, and comparing shapes. These methods and tools can be applied in a wide range of fields\, including computer vision\, biological imaging\, brain mapping\, target recognition\, and satellite image analysis. \nThis workshop is part of the NSF FRG project: Geometric and Topological Methods for Analyzing Shapes. \nThe workshop was held in room G10 of the CMSA\, located at 20 Garden Street\, Cambridge\, MA. \n\nWorkshop on Discrete Shapes\nMay 6–8\, 2022\nOrganizers: \n\nDavid Glickenstein (University of Arizona)\nJoel Hass (University of California\, Davis)\nPatrice Koehl (University of California\, Davis)\nFeng Luo (Rutgers University\, New Brunswick)\nMaria Trnkova (University of California\, Davis)\nShing-Tung Yau (Harvard)\n\nSpeakers: \n\nMiri Ben-Chen (Technion)\nAlexander Bobenko (TU Berlin)\nJohn Bowers (James Madison)\nSteven Gortler (Harvard)\nDavid Gu (Stony Brook)\nAnil Hirani (UIUC)\nYanwen Luo (Rutgers)\nPeter Schroeder (Caltech)\nJustin Solomon (MIT)\nTianqi Wu (Clark University)\n\nContributed Talk Speakers: \n\nOded Stein (MIT)\nBohan Zhou (Dartmouth)\n\nSchedule\nSchedule (PDF) \nFriday\, May 6\, 2022 \n\n\n\n\n10:00–10:05 am\n\nWelcome Opening\n\n\n10:05–10:55 am\nAnil N. Hirani\nTitle: Discrete vector bundles with connection \nAbstract: We have recently initiated a generalization of discrete exterior calculus to differential forms with values in a vector bundle. A discrete vector bundle with connection over a simplicial complex has fibers at vertices and transport maps on edges\, just as in lattice gauge theory. The first part of this work involves defining and examining properties of a combinatorial exterior covariant derivative and wedge product. We find that these operators commute with pullback under simplicial maps of the base space. From these definitions emerges a combinatorial curvature. In the second part of this work we showed that the curvature behaves as one expects: it measures failure of parallel transport to be independent of the path\, and is the local obstruction to a trivialization. For a bundle with metric\, metric compatibility of the discrete connection is equivalent to a Leibniz rule.  Vanishing curvature is indeed equivalent to an appropriately defined discrete flat connection\, and curvature obstructs trivializability. In this talk I will focus on just the first part\, and talk about naturality of the discrete exterior covariant derivative and discrete wedge product using simple examples. Joint work with Daniel Berwick-Evans (UIUC) and Mark Schubel (Apple\, Inc.).\n\n\n11:10–12:00 pm\nDavid Gu\nTitle: Surface Quadrilateral Meshing Based on Abel-Jacobi Theory \nAbstract: Surface quadrilateral meshing plays an important role in many fields. For example\, in CAD (computer-aided design)\, all shapes are represented as Spline surfaces\, which requires structured quad-meshing; in CAE (computer-aided engineering)\, the surface tessellation greatly affects the accuracy and efficiency of numerical simulations. Although the research on mesh generation has a long history\, it remains a great challenge to automatically generate structured quad-meshes with high qualities. The key is to find the governing equation for the singularities of the global structured quad-meshes. \nIn this talk\, we introduce our recent discovery:  the singularities of a quad-mesh are governed by the Abel theorem. We show that each quad-mesh determines a conformal structure and a meromorphic quadratic differential\, the configuration of the mesh singularities can be described as the divisor of the differential. The quad-mesh divisor minus four times of the divisor of a holomorphic one-form is principal and satisfies the Abel theorem: its image under the Jacobi map is zero in the Jacobi variety. \nThis leads to a rigorous and efficient algorithm for surface structured quadrilateral meshing. After determining the singularities\, the metric induced by the quad-mesh can be computed using the discrete Yambe flow\, and the meromorphic quartic differential can be constructed\, the trajectories of the differentials give the quad-mesh. The method can be applied directly for geometric modeling and computational mechanics.\n\n\n12:00–2:00 pm\nLunch Break\n\n\n\n2:00–2:50 pm\n Justin Solomon\nTitle:  Geometry Processing with Volumes \nAbstract:  Many algorithms in geometry processing are restricted to two-dimensional surfaces represented as triangle meshes.  Drawing inspiration from simulation\, medical imaging\, and other application domains\, however\, there is a substantial demand for geometry processing algorithms targeted to volumes represented as tetrahedral meshes or grids.  In this talk\, I will summarize some efforts in our group to develop a geometry processing toolkit specifically for volumes.  Specifically\, I will cover our recent work on hexahedral remeshing via cuboid decomposition\, volumetric correspondence\, and minimal surface computation via geometric measure theory.\n\n\n3:00–3:20 pm\nOded Stein\nTitle: Optimization for flip-free parametrization \nAbstract: Parametrizations without flipped elements are desirable in a variety of applications such as UV mapping and surface/volume correspondence. Computing flip-free parametrizations can be challenging\, and there are many different approaches to the problem. In this talk we will look at multiple strategies for flip-free parametrizations that are based on the optimization of continuous energies. Due to the nature of the problem\, these energies are often nonconvex and unbounded\, which is a challenge for optimization methods. We will also take a closer look at our recently developed method for computing flip-free parametrizations using the Alternating Direction Method of Multipliers (ADMM).\n\n\n3:20–4:00 pm\nBreak\n\n\n\n4:00–4:50 pm\nJohn Bowers\nTitle: Koebe-Andre’ev-Thurston Packings via Flow \nAbstract: Recently\, Connelly and Gortler gave a novel proof of the circle packing theorem for tangency packings by introducing a hybrid combinatorial-geometric operation\, flip-and-flow\, that allows two tangency packings whose contact graphs differ by a combinatorial edge flip to be continuously deformed from one to the other while maintaining tangencies across all of their common edges. Starting from a canonical tangency circle packing with the desired number of circles a finite sequence of flip-and-flow operations may be applied to obtain a circle packing for any desired (proper) contact graph with the same number of circles. \nThe full Koebe-Andre’ev-Thurston theorem generalizes the circle packing theorem to allow for neighboring circles to overlap by angles up to $\pi/2$. In this talk I will show that the Connelly-Gortler method can be extended to allow for circles to overlap to angles up to $\pi/2$. This results in a new proof of the general Koebe-Andre’ev-Thurston theorem for disk patterns on $\mathbb{S}^2$ as well as a numerical algorithm for computing them. The proof involves generalizing a notion of convexity for circle polyhedra that was recently used to prove the global rigidity of certain circle packings\, which is then used to show that all convex circle polyhedra are infinitesimally rigid\, a result of independent interest.\n\n\n5:00–5:30 pm\nMovies\n “conform!” & ”Koebe polyhedra”\n\n\n\n\n  \nSaturday\, May 7\, 2022 \n\n\n\n\n9:30–10:20 am\nAlexander Bobenko\nTitle: The Bonnet problem: Is a surface characterized by its metric and curvatures? \nAbstract: We consider a classical problem in differential geometry\, known as the Bonnet problem\, whether a surface is characterized by a metric and mean curvature function. Generically\, the answer is yes. Special cases when it is not the case are classified. In particular\, we explicitly construct a pair of immersed tori that are related by a mean curvature preserving isometry. This resolves a longstanding open problem on whether the metric and mean curvature function determine a unique compact surface. Discrete differential geometry is used to find crucial geometric properties of surfaces. This is a joint work with Tim Hoffmann and Andrew Sageman-Furnas\n\n\n10:20–11:00 am\nBreak\n\n\n\n11:00–11:50 am\nMiri Ben Chen\nTitle: Surface Multigrid via Intrinsic Prolongation \nAbstract: The solution of a linear system is a required ingredient in many geometry processing applications\, and multigrid methods are among the most efficient solution techniques. However\, due to the unstructured nature of triangle meshes\, mapping functions between different multigrid levels is challenging. In this talk I will present our recent work that uses an intrinsic prolongation operator as the main building block in a multigrid solver for curved triangle meshes. Our solver can be used as a black-box in any triangle-mesh based system that requires a linear solve\, and leads to order of magnitude time-efficiency improvement compared to direct solvers.\n\n\n12:00–2:00 pm\nLunch Break\n\n\n\n2:00–2:50 pm\nSteven Gortler\nTitle: Reconstructing configurations and graphs from unlabeled distance measurements \nAbstract: Place a configuration of n  points (vertices) generically in R^d. Measure the Euclidean lengths of m point-pairs (edges). When is the underlying graph determined by these $m$ numbers (up to isomorphism)? When is the point configuration determined by these $m$ numbers (up to congruence)? This question is motivated by a number of inverse problem applications. In this talk\, I will review what is known about this question.\n\n\n3:00–3:20 pm\nBohan Zhou\nTitle: Efficient and Exact Multimarginal Optimal Transport with Pairwise Costs \nAbstract: Optimal transport has profound and wide applications since its introduction in 1781 by Monge. Thanks to the Benamou-Brenier formulation\, it provides a meaningful functional in the image science like image and shape registrations. However\, exact computation through LP or PDE is in general not practical in large scale\, while the popular entropy-regularized method introduces additional diffusion noise\, deteriorating shapes and boundaries. Until the recent work [Jacobs and Leger\, A Fast Approach to Optimal Transport: the back-and-forth method\, Numerische Mathematik\, 2020]\, solving OT in a both accurate and fast fashion finally becomes possible. Multiple marginal optimal transport is a natural extension from OT but has its own interest and is in general more computationally expensive. The entropy method suffers from both diffusion noise and high dimensional computational issues. In this work with Matthew Parno\, we extend from two marginals to multiple marginals\, on a wide class of cost functions when those marginals have a graph structure. This new method is fast and does not introduce diffusion. As a result\, the new proposed method can be used in many fields those require sharp boundaries. If time allows\, we will illustrate by examples the faithful joint recover via MMOT of images with sharp boundaries\, with applications on sea ice prediction.\n\n\n3:20–4:00 pm\nBreak\n\n\n\n4:00–4:50 pm\nPeter Schroeder\nTitle: Constrained Willmore Surfaces \nAbstract: The Willmore energy of a surface is a canonical example of a squared curvature bending energy. Its minimizers are therefore of interest both in the theory of surfaces and in practical applications from physical and geometric modeling. Minimizing the bending energy alone however is insufficient. Taking a cue from univariate splines which incorporate an isometry constraint we consider Willmore minimizers subject to a conformality constraint. In this talk I will report on a numerical algorithm to find such constrained minimizers for triangle meshes. \nJoint work with Yousuf Soliman (Caltech)\, Olga Diamanti (UGraz)\, Albert Chern (UCSD)\, Felix Knöppel (TU Berlin)\, Ulrich Pinkall (TU Berlin).\n\n\n5:00–5:50 pm\n\nProblems and Application discussions\n\n\n\n\n  \nSunday\, May 8\, 2022 \n\n\n\n\n9:00–9:50 am\nTianqi Wu\nTitle: Convergence of discrete uniformizations \nAbstract: The theory of discrete conformality\, based on the notion of vertex scaling\, has been implemented in computing conformal maps or uniformizations of surfaces. We will show that if a Delaunay triangle mesh approximates a smooth surface\, then the related discrete uniformization will converge to the smooth uniformization\, with an error bounded linearly by the size of the triangles in the mesh.\n\n\n10:10–11:00 am\nYanwen Luo\nTitle:  Recent Progress in Spaces of Geodesic Triangulations of Surfaces\n\nAbstract: Spaces of geodesic triangulations of surfaces are natural discretization of the groups of surface diffeomorphisms isotopy to the identity. It has been conjectured that these spaces have the same homotopy type as their smooth counterparts. In this talk\, we will report the recent progress in this problem. The key ingredient is the idea in Tutte’s embedding theorem. We will explain how to use it to identify the homotopy types of spaces of geodesic triangulations. This is joint work with Tianqi Wu and Xiaoping Zhu.\n\n\n11:10–12:00 pm\n\nProblems and Application discussions\n\n\n12:00–1:00 pm\nMovie\n“The Discrete Charm of Geometry”
URL:https://cmsa.fas.harvard.edu/event/2022-nsf-frg-workshop/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
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