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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211001T093000
DTEND;TZID=America/New_York:20211001T103000
DTSTAMP:20260510T115118
CREATED:20240214T074545Z
LAST-MODIFIED:20240301T111944Z
UID:10002569-1633080600-1633084200@cmsa.fas.harvard.edu
SUMMARY:Instability of naked singularities in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Jue Liu \nTitle: Instability of naked singularities in general relativity \nAbstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture\, proposed by Penrose\, which roughly states that for generic physical spacetime\, the singularities (if existed) must be hidden behind the black holes. Unfortunately\, the singularities visible to faraway observers\, which are called by naked singularities\, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime\, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases\, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method\, and it is this wild method that helps us to extend some results to the asymmetric cases.
URL:https://cmsa.fas.harvard.edu/event/10-1-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211001T093000
DTEND;TZID=America/New_York:20211001T103000
DTSTAMP:20260510T115118
CREATED:20240304T101543Z
LAST-MODIFIED:20240304T101543Z
UID:10002898-1633080600-1633084200@cmsa.fas.harvard.edu
SUMMARY:Static vacuum extensions of Bartnik boundary data near flat domains
DESCRIPTION:Abstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation\, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.
URL:https://cmsa.fas.harvard.edu/event/10-1-2021-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211004T025100
DTEND;TZID=America/New_York:20211005T025100
DTSTAMP:20260510T115118
CREATED:20230705T081940Z
LAST-MODIFIED:20250328T200226Z
UID:10000071-1633315860-1633402260@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott
DESCRIPTION:On October 4th and October 5th\, 2021\, Harvard CMSA will host its annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker will be Michael Freedman (Microsoft). The lectures will take place from 11:00am – 12:15pm (ET) on Zoom. \nThis will be the third annual lecture series held in honor of Raoul Bott. \n\n\n\n\nLecture 1\nOctober 4th\, 11:00am (Boston time)\nTitle: The Universe from a single Particle \nAbstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler\, single particle\, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini\, see arXiv:2011.05917 and arXiv:2108.12709. \nVideo\n\n\nLecture 2\nOctober 5th\, 11:00am (Boston time)\nTitle: Controlled Mather Thurston Theorems. \nAbstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms\, semi-s-cobordisms\, are required. In physical applications\, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374   \nVideo\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/math-science-lectures-in-honor-of-raoul-bott/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Public Lecture,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211004T110000
DTEND;TZID=America/New_York:20211004T123000
DTSTAMP:20260510T115118
CREATED:20240212T110410Z
LAST-MODIFIED:20250409T192600Z
UID:10002032-1633345200-1633350600@cmsa.fas.harvard.edu
SUMMARY:Math Science Lectures in Honor of Raoul Bott: Michael Freedman
DESCRIPTION:On October 4th and October 5th\, 2021\, Harvard CMSA hosted the annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker was Michael Freedman (Microsoft). The lectures took place on Zoom. \nThis will be the third annual lecture series held in honor of Raoul Bott. \n\n\n\n\nLecture 1\nOctober 4th\, 11:00am (Boston time)\nTitle: The Universe from a single Particle \nAbstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler\, single particle\, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini\, see arXiv:2011.05917 and arXiv:2108.12709. \nVideo\n\n\nLecture 2\nOctober 5th\, 11:00am (Boston time)\nTitle: Controlled Mather Thurston Theorems. \nAbstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms\, semi-s-cobordisms\, are required. In physical applications\, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374   \nVideo\n\n\n\n 
URL:https://cmsa.fas.harvard.edu/event/math-science-lectures-in-honor-of-raoul-bott-3/
LOCATION:Virtual
CATEGORIES:Event,Math Science Lectures in Honor of Raoul Bott,Special Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211005T083000
DTEND;TZID=America/New_York:20211005T093000
DTSTAMP:20260510T115118
CREATED:20240213T111744Z
LAST-MODIFIED:20240304T104852Z
UID:10002487-1633422600-1633426200@cmsa.fas.harvard.edu
SUMMARY:Angular momentum in general relativity
DESCRIPTION:Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′\, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk\, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term\, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen\, Jordan Keller\, Ye-Kai Wang\, and Shing-Tung Yau.
URL:https://cmsa.fas.harvard.edu/event/10-5-2021-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211005T090000
DTEND;TZID=America/New_York:20211005T100000
DTSTAMP:20260510T115118
CREATED:20240213T113617Z
LAST-MODIFIED:20240304T085033Z
UID:10002508-1633424400-1633428000@cmsa.fas.harvard.edu
SUMMARY:10/5/2021 Combinatorics\, Physics and Probability Seminar
DESCRIPTION:Title: Geodesic Geometry on Graphs \nAbstract: In a graph G = (V\, E) we consider a system of paths S so that for every two vertices u\,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths\, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case\, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w. \nWe’ll discuss the concept of graph metrizability\, and\, in particular\, we’ll see that while metrizability is a rare property\, there exists infinitely many 2-connected metrizable graphs. \nJoint work with Nati Linial.
URL:https://cmsa.fas.harvard.edu/event/10-5-2021-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T093000
DTEND;TZID=America/New_York:20211006T103000
DTSTAMP:20260510T115118
CREATED:20240214T044013Z
LAST-MODIFIED:20240501T205719Z
UID:10002532-1633512600-1633516200@cmsa.fas.harvard.edu
SUMMARY:Strings\, knots and quivers
DESCRIPTION:Speaker: Piotr Sułkowski (University of 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.
URL:https://cmsa.fas.harvard.edu/event/strings-knots-and-quivers/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T114900
DTEND;TZID=America/New_York:20211006T134900
DTSTAMP:20260510T115118
CREATED:20240214T090718Z
LAST-MODIFIED:20240301T093241Z
UID:10002606-1633520940-1633528140@cmsa.fas.harvard.edu
SUMMARY:Line defects in CFTs: Renormalization group flows and semiclassical limits
DESCRIPTION:Title: Line defects in CFTs: Renormalization group flows and semiclassical limits \nAbstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk\, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk\, I will present some applications. In particular\, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down\, and these are studied in a semiclassical expansion at fixed epsilon S.
URL:https://cmsa.fas.harvard.edu/event/10-6-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T150000
DTEND;TZID=America/New_York:20211006T160000
DTSTAMP:20260510T115118
CREATED:20240214T092921Z
LAST-MODIFIED:20240517T200621Z
UID:10002630-1633532400-1633536000@cmsa.fas.harvard.edu
SUMMARY:New results in Supergravity via ML Technology
DESCRIPTION:Speaker: Thomas Fischbacher\, Google \nTitle: New results in Supergravity via ML Technology \nAbstract: The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library\, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions\, has allowed major progress on other related questions about M theory\, and briefly discuss other applications in field theory and beyond.
URL:https://cmsa.fas.harvard.edu/event/10-6-2021-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211007T115400
DTEND;TZID=America/New_York:20211007T135400
DTSTAMP:20260510T115118
CREATED:20240214T090253Z
LAST-MODIFIED:20240301T092837Z
UID:10002604-1633607640-1633614840@cmsa.fas.harvard.edu
SUMMARY:A tour of categorical symmetry
DESCRIPTION:Title: A tour of categorical symmetry \nAbstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”\, their applications\, and some open problems.
URL:https://cmsa.fas.harvard.edu/event/10-7-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211007T130000
DTEND;TZID=America/New_York:20211007T140000
DTSTAMP:20260510T115118
CREATED:20240214T053935Z
LAST-MODIFIED:20240304T063527Z
UID:10002541-1633611600-1633615200@cmsa.fas.harvard.edu
SUMMARY:A mirror theorem for GLSMs
DESCRIPTION:Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V\, a group G acting on V\, a character \theta of G\, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts\, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory\, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM\, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.
URL:https://cmsa.fas.harvard.edu/event/a-mirror-theorem-for-glsms/
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211007T184100
DTEND;TZID=America/New_York:20211007T184100
DTSTAMP:20260510T115118
CREATED:20240214T083403Z
LAST-MODIFIED:20240214T083403Z
UID:10002590-1633632060-1633632060@cmsa.fas.harvard.edu
SUMMARY:10/7/2021 Interdisciplinary Science Seminar
DESCRIPTION:Title: SiRNA Targeting TCRb: A Proposed Therapy for the Treatment of Autoimmunity \nAbstract: As of 2018\, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent\, treatment options remain relatively poor\, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness over time. Given this\, new forms of therapy are needed. To this end\, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted\, novel means of therapy for the treatment of autoimmune disorders. \nThis talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally\, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.
URL:https://cmsa.fas.harvard.edu/event/10-7-2021-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211007T203000
DTEND;TZID=America/New_York:20211007T220000
DTSTAMP:20260510T115118
CREATED:20240301T093101Z
LAST-MODIFIED:20240301T093101Z
UID:10002891-1633638600-1633644000@cmsa.fas.harvard.edu
SUMMARY:UV/IR and Effective Field Theory
DESCRIPTION:Speaker: Nima Arkani-Hamed (IAS Princeton) \nTitle: UV/IR and Effective Field Theory
URL:https://cmsa.fas.harvard.edu/event/10-7-2021-quantum-matter-in-mathematics-and-physics-2/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211008T093000
DTEND;TZID=America/New_York:20211008T103000
DTSTAMP:20260510T115118
CREATED:20240213T110012Z
LAST-MODIFIED:20240304T101810Z
UID:10002469-1633685400-1633689000@cmsa.fas.harvard.edu
SUMMARY:Causality Comparison and Postive Mass
DESCRIPTION:Speaker: Xiaoning Wu\, Chinese Academy of Sciences \nTitle: Causality Comparison and Postive Mass \nAbstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper\, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new\, substantially simple\, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity
URL:https://cmsa.fas.harvard.edu/event/10-8-2021-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211008T093000
DTEND;TZID=America/New_York:20211008T103000
DTSTAMP:20260510T115118
CREATED:20240214T074201Z
LAST-MODIFIED:20240301T111834Z
UID:10002568-1633685400-1633689000@cmsa.fas.harvard.edu
SUMMARY:Knowledge Graph Embeddings and Inference
DESCRIPTION:Member Seminar \nSpeaker: Michael Douglas \nTitle: Knowledge Graph Embeddings and Inference \nAbstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.\nA popular KG representation method is graph embedding\, which facilitates question answering\, inferring missing edges\, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning\, network learning\, and unstructured statistical inference\, and describe experiments to measure the contributions of each mechanism. \nJoint work with M. Simkin\, O. Ben-Eliezer\, T. Wu\, S. P. Chin\, T. V. Dang and A. Wood.
URL:https://cmsa.fas.harvard.edu/event/10-8-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211012T090000
DTEND;TZID=America/New_York:20211012T100000
DTSTAMP:20260510T115118
CREATED:20240213T114547Z
LAST-MODIFIED:20240304T100222Z
UID:10002513-1634029200-1634032800@cmsa.fas.harvard.edu
SUMMARY:10/12/2021 Combinatorics\, Physics and Probability Seminar
DESCRIPTION:Title: On counting algebraically defined graphs \nAbstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane)\, the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes\, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials)\, and this lower bound essentially matches the upper bound from Warren’s theorem.
URL:https://cmsa.fas.harvard.edu/event/10-12-2021-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211012T130000
DTEND;TZID=America/New_York:20211012T140000
DTSTAMP:20260510T115118
CREATED:20240214T053342Z
LAST-MODIFIED:20240304T063443Z
UID:10002540-1634043600-1634047200@cmsa.fas.harvard.edu
SUMMARY:Derived projectivizations of two-term complexes
DESCRIPTION:Abstract: For a given two-term complex of vector bundles on a derived scheme (or stack)\, there are three natural ways to define its “derived projectivizations”: (i) as the derived base-change of the classical projectivization of Grothendieck; (ii) as the derived moduli parametrizing one-dimensional locally free quotients; (iii) as the GIT quotient of the total space by $\mathbb{G}_m$-action. In this talk\, we first show that these three definitions are equivalent. Second\, we prove a structural theorem about the derived categories of derived projectivizations and study the corresponding mutation theory. Third\, we apply these results to various moduli situations\, including the moduli of certain stable pairs on curves and the Hecke correspondences of one-point modification of moduli of stable sheaves on surfaces. If time allowed\, we could also discuss the generalizations of these results to the derived Quot schemes of locally free quotients.
URL:https://cmsa.fas.harvard.edu/event/derived-projectivizations-of-two-term-complexes/
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211013T030000
DTEND;TZID=America/New_York:20211013T040000
DTSTAMP:20260510T115118
CREATED:20240213T113713Z
LAST-MODIFIED:20240304T100928Z
UID:10002509-1634094000-1634097600@cmsa.fas.harvard.edu
SUMMARY:Some remarks on contact Calabi-Yau 7-manifolds
DESCRIPTION:Abstract: In geometry and physics it has proved useful to relate G2 and Calabi-Yau geometry via circle bundles. Contact Calabi-Yau 7-manifolds are\, in the simplest cases\, such circle bundles over Calabi-Yau 3-orbifolds. These 7-manifolds provide testing grounds for the study of geometric flows which seek to find torsion-free G2-structures (and thus Ricci flat metrics with exceptional holonomy). They also give useful backgrounds to examine the heterotic G2 system (also known as the G2-Hull-Strominger system)\, which is a coupled set of PDEs arising from physics that involves the G2-structure and gauge theory on the 7-manifold. I will report on recent progress on both of these directions in the study of contact Calabi-Yau 7-manifolds\, which is joint work with H. Sá Earp and J. Saavedra.
URL:https://cmsa.fas.harvard.edu/event/10-13-2021-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211013T093000
DTEND;TZID=America/New_York:20211013T103000
DTSTAMP:20260510T115118
CREATED:20240214T043728Z
LAST-MODIFIED:20240507T193448Z
UID:10002531-1634117400-1634121000@cmsa.fas.harvard.edu
SUMMARY:Knot homology and sheaves on the Hilbert scheme of points on the plane
DESCRIPTION:Speaker: Alexei 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.
URL:https://cmsa.fas.harvard.edu/event/knot-homology-and-sheaves-on-the-hilbert-scheme-of-points-on-the-plane/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.13.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211013T140000
DTEND;TZID=America/New_York:20211013T150000
DTSTAMP:20260510T115118
CREATED:20240214T093531Z
LAST-MODIFIED:20240515T204354Z
UID:10002637-1634133600-1634137200@cmsa.fas.harvard.edu
SUMMARY:Computer-Aided Mathematics and Satisfiability
DESCRIPTION:Speaker: Marijn Heule\, Carnegie Mellon University \nTitle: Computer-Aided Mathematics and Satisfiability \nAbstract: Progress in satisfiability (SAT) solving has made it possible to determine the correctness of complex systems and answer long-standing open questions in mathematics. The SAT solving approach is completely automatic and can produce clever though potentially gigantic proofs. We can have confidence in the correctness of the answers because highly trustworthy systems can validate the underlying proofs regardless of their size. We demonstrate the effectiveness of the SAT approach by presenting some recent successes\, including the solution of the Boolean Pythagorean Triples problem\, computing the fifth Schur number\, and resolving the remaining case of Keller’s conjecture. Moreover\, we constructed and validated a proof for each of these results. The second part of the talk focuses on notorious math challenges for which automated reasoning may well be suitable. In particular\, we discuss our progress on applying SAT solving techniques to the chromatic number of the plane (Hadwiger-Nelson problem)\, optimal schemes for matrix multiplication\, and the Collatz conjecture.
URL:https://cmsa.fas.harvard.edu/event/10-13-2021-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211014T090000
DTEND;TZID=America/New_York:20211014T100000
DTSTAMP:20260510T115118
CREATED:20240214T082843Z
LAST-MODIFIED:20240529T180858Z
UID:10002588-1634202000-1634205600@cmsa.fas.harvard.edu
SUMMARY:D3C: Reducing the Price of Anarchy in Multi-Agent Learning
DESCRIPTION:Speaker: Ian Gemp\, DeepMind \nTitle: D3C: Reducing the Price of Anarchy in Multi-Agent Learning \nAbstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.
URL:https://cmsa.fas.harvard.edu/event/10-14-2021-interdisciplinary-science-seminar/
LOCATION:Virtual
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-10.14.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211014T130000
DTEND;TZID=America/New_York:20211014T143000
DTSTAMP:20260510T115118
CREATED:20240213T113426Z
LAST-MODIFIED:20240304T084942Z
UID:10002506-1634216400-1634221800@cmsa.fas.harvard.edu
SUMMARY:Stochastic PDE as scaling limits of interacting particle systems
DESCRIPTION:Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details\, including randomness and discreteness of individuals\, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk\, I will illustrate how this challenge can be overcome by elucidating the probabilistic connections between models of different levels of detail. These connections explain how stochastic partial differential equations (SPDE) arise naturally from particle models. \nI will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE\, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and duality formulas are obtained for these SPDE\, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.
URL:https://cmsa.fas.harvard.edu/event/stochastic-pde-as-scaling-limits-of-interacting-particle-systems/
CATEGORIES:Active Matter Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211015T093000
DTEND;TZID=America/New_York:20211015T103000
DTSTAMP:20260510T115118
CREATED:20240213T105113Z
LAST-MODIFIED:20240304T101004Z
UID:10002463-1634290200-1634293800@cmsa.fas.harvard.edu
SUMMARY:Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations
DESCRIPTION:Abstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint\, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism\, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.
URL:https://cmsa.fas.harvard.edu/event/10-15-2021-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211015T093000
DTEND;TZID=America/New_York:20211015T103000
DTSTAMP:20260510T115118
CREATED:20240214T073928Z
LAST-MODIFIED:20240301T111732Z
UID:10002566-1634290200-1634293800@cmsa.fas.harvard.edu
SUMMARY:C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model \nAbstract: Discrete spacetime symmetries of parity P or reflection R\, and time-reversal T\, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F\, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures\, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT)\, or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320. \nIn the second part of my talk\, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition\, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.
URL:https://cmsa.fas.harvard.edu/event/10-15-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211015T103000
DTEND;TZID=America/New_York:20211015T113000
DTSTAMP:20260510T115118
CREATED:20240125T164122Z
LAST-MODIFIED:20240125T164122Z
UID:10001336-1634293800-1634297400@cmsa.fas.harvard.edu
SUMMARY:General Relativity 2021-22
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a seminar on General Relativity\, organized by Aghil Alaee\, Jue Liu\, Daniel Kapec\, and Puskar Mondal. This seminar will take place on Thursdays at 9:30am – 10:30am (Eastern time). The meetings will take place virtually on Zoom. To learn how to attend\, please fill out this form. \nThe schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n2/10/2022\nTin Yau Tsang (UC Irvine)\nTitle: Dihedral ridigity and mass \nAbstract: To characterise scalar curvature\, Gromov proposed the dihedral rigidity conjecture which states that a positively curved polyhedron having dihedral angles less than those of a corresponding flat polyhedron should be isometric to a flat one. In this talk\, we will discuss some recent progress on this conjecture and its connection with general relativity (ADM mass and quasilocal mass).\n\n\n2/17/2022\nShiraz Minwalla\n(Tata Institute of Fundamental Research\, Mumbai)\nTitle: Black Hole dynamics at Large D \nAbstract: I demonstrate that black hole dynamics simplifies – without trivializing – in the limit in which the number of spacetime dimensions D in which the black holes live is taken to infinity. In the strict large D limit and under certain conditions I show the equations that govern black hole dynamics reduce to the equations describing the dynamics of a non gravitational membrane propagating in an unperturbed spacetime (e.g. flat space). In the stationary limit black hole thermodynamics maps to membrane thermodynamics\, which we formulate in a precise manner. We also demonstrate that the large D black hole membrane agrees with the fluid gravity map in the appropriate regime.\n\n\n2/24/2022\nAchilleas Porfyriadis\n(Harvard Black Hole Initiative)\nTitle: Extreme Black Holes: Anabasis and Accidental Symmetry \nAbstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of  AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2) transformation properties of the spherically symmetric linear perturbations of\nAdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2\, with or without additional matter\, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of  AdS_2.\n\n\n3/10/2022\nDavid Fajman (University of Vienna)\nTitle: The Einstein-flow on manifolds of negative curvature\n\nAbstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes\, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations\, how they can be handled depending on the matter model at hand\, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.\n\n\n3/21/2022\nProf. Arick Shao (Queen Mary University of London)\nTitle: Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes \nAbstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation\, we prove rigorous mathematical statements toward this conjecture. \nIn particular\, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result\, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. \nThis is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).\n\n\n3/24/2022\nQian Wang\, University of Oxford\nTitle: Rough solutions of the $3$-D compressible Euler equations \nAbstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D\, for the Cauchy data of the velocity\, density and vorticity $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang\, established in the irrotational case\, i.e $\omega=0$\, which is known to be optimal for $s>2$. At the opposite extreme\, in the incompressible case\, i.e. with a constant density\,  the result is known to hold for $\omega\in H^s$\, $s>3/2$ and fails for $s\le 3/2$\, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $s>2\, \\, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves\, governed by quasilinear wave equations\, and vorticity which is transported by the flow. To overcome this difficulty\, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.\n\n\n3/28/2022\nEmanuele Berti\, Johns Hopkins University\nTitle: Black Hole Spectroscopy \nAbstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?\n\n\n4/7/2022\n\nCMSA General Relativity Conference\n\n\n4/14/2022\nChao Liu\, Huazhong University of Science and Technology\nTitle: Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4 \nAbstract: In this talk\, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.\n\n\n4/21/2022\nJinhua Wang\,\nXiamen University\nTitle: Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system \nAbstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability\, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof\, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover\, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.\n\n\n4/28/2022\nAllen Fang\, Sorbonne University\nTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter \nAbstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk\, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vectorfield techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/10/2021 \n(10:30am – 11:30am (Boston time)\nPhilippe G. LeFloch\, Sorbonne University and CNRS\nTitle: Asymptotic localization\, massive fields\, and gravitational singularities \nAbstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First\, the Seed-to-Solution Method for Einstein’s constraint equations\, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass\, Schwarzschild decay\, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second\, the Euclidian-Hyperboloidal Foliation Method\, introduced in collaboration with Yue Ma\, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third\, in collaboration with Bruno Le Floch and Gabriele Veneziano\, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and\, by analyzing Einstein’s constraint equations\, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org\n\n\n9/17/2021 \n(10:30am – 11:30am (Boston time)\nIgor Rodnianski\, Princeton University\nTitle: Stable Big Bang formation for the Einstein equations \nAbstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature\, going back more than 50 years\, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data\, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents\, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.\n\n\n9/24/2021 \n(10:30am – 11:30am (Boston time)\nAlex Lupsasca\nTitle: On the Observable Shape of Black Hole Photon Rings \nAbstract: The photon ring is a narrow ring-shaped feature\, predicted by General Relativity but not yet observed\, that appears on images of sources near a black hole. It is caused by extreme bending of light within a few Schwarzschild radii of the event horizon and provides a direct probe of the unstable bound photon orbits of the Kerr geometry. I will argue that the precise shape of the observable photon ring is remarkably insensitive to the astronomical source profile and can therefore be used as a stringent test of strong-field General Relativity. In practice\, near-term interferometric observations may be limited to the visibility amplitude alone\, which contains incomplete shape information: for convex curves\, the amplitude only encodes the set of projected diameters (or “widths”) of the shape. I will describe the freedom in reconstructing a convex curve from its widths\, giving insight into the photon ring shape information probed by technically plausible future astronomical measurements.\n\n\n10/1/2021 \n(10:30am – 11:30am (Boston time)\nZhongshan An\, University of Connecticut\nTitle: Static vacuum extensions of Bartnik boundary data near flat domains \nAbstract: The study of static vacuum Riemannian metrics arises naturally in differential geometry and general relativity. It plays an important role in scalar curvature deformation\, as well as in constructing Einstein spacetimes.  Existence of static vacuum Riemannian metrics with prescribed Bartnik data is one of the most fundamental problems in Riemannian geometry related to general relativity. It is also a very interesting problem on the global solvability of a natural geometric boundary value problem. In this talk I will first discuss some basic properties of the nonlinear and linearized static vacuum equations and the geometric boundary conditions. Then I will present some recent progress towards the existence problem of static vacuum metrics based on a joint work with Lan-Hsuan Huang.\n\n\n10/8/2021 \n(10:30am – 11:30am (Boston time)\nXiaoning Wu\, Chinese Academy of Sciences\nTitle: Causality Comparison and Postive Mass \nAbstract: Penrose et al. investigated the physical incoherence of the space-time with negative mass via the bending of light. Precise estimates of the time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper\, we construct an intermediate diagonal metric and reduce this problem to a causality comparison in the compactified space-time regarding time-like connectedness near conformal infinities. This different approach allows us to avoid encountering the difficulties and subtle issues that Penrose et al. met. It provides a new\, substantially simple\, and physically natural non-partial differential equation viewpoint to understand the positive mass theorem. This elementary argument modestly applies to asymptotically flat solutions that are vacuum and stationary near infinity\n\n\n10/15/2021 \n(10:30am – 11:30am (Boston time)\nJiong-Yue Li\, Sun Yat-Sen University\nTitle: Peeling properties of the spinor fields and the solutions to nonlinear Dirac equations \nAbstract: The Dirac equation is a relativistic equation that describes the spin-1/2 particles.  We talk about Dirac equations in Minkowski spacetime. In a geometric viewpoint\, we can see that the spinor fields satisfying the Dirac equations enjoy the so-called peeling properties. It means the null components of the solution will decay at different rates along the null hypersurface. Based on this decay mechanism\, we can obtain a fresh insight to the spinor null forms which is used to prove a small data global existence result especially for some quadratic Dirac models.\n\n\n10/22/2021 \n(11:00am – 12:30pm (Boston time)\nRoberto Emparan\, University of Barcelona\nTitle: The Large D Limit of Einstein’s Equations \nAbstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study\, with relatively simple techniques\, some of the thorniest problems in black hole physics\, such as the non-linear evolution of the instabilities of black strings and black branes\, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about\, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.\n\n\n10/28/2021\nJorge Santos\, University of Cambridge\nTitle: The classical interior of charged black holes with AdS asymptotics \nAbstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations\, Cauchy horizons never form. We then consider charged scalars\, which are known to condense at low temperatures\, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity\, and there is no Cauchy horizon. Before reaching the singularity\, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion\, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations\, the number of Kasner inversions depends very sensitively on temperature\, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures\, the final Kasner exponent exhibits fractal-like behavior.\n\n\n11/4/2021\nat 10 am ET\nElena Giorgi\, Columbia University\nTitle: The stability of charged black holes \nAbstract: Black holes 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\n11/11/2021\n*9:30 am ET*\nSiyuan Ma\, Sorbonne University\nTitle: Sharp decay for Teukolsky equation in Kerr spacetimes \nAbstract: Teukolsky equation in Kerr spacetimes governs the dynamics of the spin $s$ components\, $s=0\, \pm 1\, \pm 2$ corresponding to the scalar field\, the Maxwell field\, and the linearized gravity\, respectively. I will discuss recent joint work with L. Zhang on proving the precise asymptotic profiles for these spin $s$ components in Schwarzschild and Kerr spacetimes.\n\n\n11/19/2021 \n(10:30–11:30 am ET)\nNishanth Gudapati\, Clark University\nTitle: On Curvature Propagation and ‘Breakdown’ of the Einstein Equations on U(1) Symmetric Spacetimes \nAbstract: The analysis of global structure of the Einstein equations for general relativity\, in the context of the initial value problem\, is a difficult and intricate mathematical subject. Any additional structure in their formulation is welcome\, in order to alleviate the problem.  It is expected that the initial value problem of the Einstein equations on spacetimes admitting a translational\, fixed-point free\, spatial U(1) isometry group are globally well-posed. In our previous works\, we discussed the special structure provided by the dimensional reduction of 3+1 dimensional U(1) symmetric Einstein equations to 2+1 Einstein-wave map system and demonstrated global existence in the equivariant case for large data.  In this talk\, after discussing some preliminaries and background\, we shall discuss about yet another structure of the U(1) symmetric Einstein equations\, namely the analogy with Yang-Mills theory via the Cartan formalism and reconcile with the dimensionally reduced field equations. We shall also discuss implications for ‘breakdown’ criteria of U(1) symmetric Einstein equations.\n\n\n12/2/2021\nProfessor Geoffrey Comp\nére\, Université Libre de Bruxelles\nTitle: Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger \nAbstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion\, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.\n\n\n12/16/2021\nXinliang An\, University of Singapore\nTitle: Low regularity ill-posedness for 3D elastic waves and for 3D ideal compressible MHD driven by shock formation \nAbstract: We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three spatial dimensions (3D). Inspired by the recent works of Christodoulou\, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3(R^3)$ and $H^2(R^3)$\, respectively. Both elastic waves and MHD are physical systems with multiple wave speeds.  We further prove that the ill-posedness is caused by instantaneous shock formation\, which is characterized by the vanishing of the inverse foliation density. In particular\, when the magnetic field is absent in MHD\, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations\, and it is sharp with respect to the regularity of the fluid velocity.  Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. To trace the nonlinear interactions of various waves\, we algebraically decompose the 3D elastic waves and the 3D ideal MHD equations into $6\times 6$ and $7\times 7$ non-strictly hyperbolic systems. Via detailed calculations\, we reveal their hidden subtle structures. With them\, we give a complete description of solutions’ dynamics up to the earliest singular event\, when a shock forms. This talk is based on joint works with Haoyang Chen and Silu Yin.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-2021-22/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211018T130000
DTEND;TZID=America/New_York:20211018T140000
DTSTAMP:20260510T115118
CREATED:20240214T093528Z
LAST-MODIFIED:20240301T082954Z
UID:10002636-1634562000-1634565600@cmsa.fas.harvard.edu
SUMMARY:The Festina Lente Bound
DESCRIPTION:Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology\, both top-down and bottom-up.
URL:https://cmsa.fas.harvard.edu/event/10-18-2021-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211019T090000
DTEND;TZID=America/New_York:20211019T100000
DTSTAMP:20260510T115118
CREATED:20240213T114112Z
LAST-MODIFIED:20240304T100424Z
UID:10002511-1634634000-1634637600@cmsa.fas.harvard.edu
SUMMARY:10/19/2021 Combinatorics\, Physics and Probability Seminar
DESCRIPTION:Title: Ising model\, total positivity\, and criticality \nAbstract: The Ising model\, introduced in 1920\, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature\, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.\nThe totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases\, and is closely related to cluster algebras and scattering amplitudes.\nI will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian\, obtained in our recent work with P. Pylyavskyy. Building on this connection\, I will give a new boundary correlation formula for the critical Ising model
URL:https://cmsa.fas.harvard.edu/event/10-19-2021-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211019T130000
DTEND;TZID=America/New_York:20211019T140000
DTSTAMP:20260510T115118
CREATED:20240214T053044Z
LAST-MODIFIED:20240304T063307Z
UID:10002539-1634648400-1634652000@cmsa.fas.harvard.edu
SUMMARY:D-critical structure(s) on Quot schemes of points of Calabi-Yau 3-folds
DESCRIPTION:Abstract: D-critical schemes and Artin stacks were introduced by Joyce in 2015\, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes\, but the problem of constructing the d-critical structure on a “DT moduli space” without passing through derived geometry is wide open. We discuss this problem\, and new results in this direction\, when the moduli space is the Hilbert (or Quot) scheme of points on a Calabi-Yau 3-fold. Joint work with Michail Savvas.
URL:https://cmsa.fas.harvard.edu/event/d-critical-structures-on-quot-schemes-of-points-of-calabi-yau-3-folds/
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211019T203000
DTEND;TZID=America/New_York:20211019T213000
DTSTAMP:20260510T115118
CREATED:20240304T103826Z
LAST-MODIFIED:20240304T103826Z
UID:10002901-1634675400-1634679000@cmsa.fas.harvard.edu
SUMMARY:Tropical disk counts
DESCRIPTION:Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application\, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.
URL:https://cmsa.fas.harvard.edu/event/10-19-2021-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211020T093000
DTEND;TZID=America/New_York:20211020T103000
DTSTAMP:20260510T115118
CREATED:20240214T043359Z
LAST-MODIFIED:20240507T193206Z
UID:10002530-1634722200-1634725800@cmsa.fas.harvard.edu
SUMMARY:Categorification and applications
DESCRIPTION:Speaker: Peng Shan (Tsinghua University)\n\n\n\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.
URL:https://cmsa.fas.harvard.edu/event/categorification-and-applications/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.20.21.png
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END:VCALENDAR