BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CMSA - ECPv6.15.20//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:CMSA X-ORIGINAL-URL:https://cmsa.fas.harvard.edu X-WR-CALDESC:Events for CMSA REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/New_York BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20200308T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20201101T060000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20210314T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20211107T060000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:EDT DTSTART:20220313T070000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:EST DTSTART:20221106T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/New_York:20211013T030000 DTEND;TZID=America/New_York:20211013T040000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211013T093000 DTEND;TZID=America/New_York:20211013T103000 DTSTAMP:20260510T020118 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/ LOCATION:MA 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:20260510T020118 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/ LOCATION:MA CATEGORIES:New Technologies in Mathematics Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211014T090000 DTEND;TZID=America/New_York:20211014T100000 DTSTAMP:20260510T020118 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:20260510T020118 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/ LOCATION:MA CATEGORIES:Active Matter Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211015T093000 DTEND;TZID=America/New_York:20211015T103000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211015T093000 DTEND;TZID=America/New_York:20211015T103000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Member Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211015T103000 DTEND;TZID=America/New_York:20211015T113000 DTSTAMP:20260510T020118 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 $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $22$. 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/ LOCATION:MA CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211018T130000 DTEND;TZID=America/New_York:20211018T140000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Swampland Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211019T090000 DTEND;TZID=America/New_York:20211019T100000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Combinatorics Physics and Probability END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211019T130000 DTEND;TZID=America/New_York:20211019T140000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Algebraic Geometry in String Theory Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211019T203000 DTEND;TZID=America/New_York:20211019T213000 DTSTAMP:20260510T020118 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/ LOCATION:MA CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211020T093000 DTEND;TZID=America/New_York:20211020T103000 DTSTAMP:20260510T020118 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 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211021T153000 DTEND;TZID=America/New_York:20211021T170000 DTSTAMP:20260510T020118 CREATED:20240214T102900Z LAST-MODIFIED:20240301T091902Z UID:10002672-1634830200-1634835600@cmsa.fas.harvard.edu SUMMARY:Electric-magnetic duality and the Geometric Langlands duality DESCRIPTION:Title: Electric-magnetic duality and the Geometric Langlands duality \nAbstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality. URL:https://cmsa.fas.harvard.edu/event/10-21-2021-quantum-matter-in-mathematics-and-physics/ LOCATION:Virtual CATEGORIES:Quantum Matter END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211021T184400 DTEND;TZID=America/New_York:20211021T204400 DTSTAMP:20260510T020118 CREATED:20240214T082555Z LAST-MODIFIED:20240301T104328Z UID:10002587-1634841840-1634849040@cmsa.fas.harvard.edu SUMMARY:10/21/2021 Interdisciplinary Science Seminar DESCRIPTION:Title: Mathematical resolution of the Liouville conformal field theory. \nAbstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David\, Kupiainen\, Rhodes\, Vargas. \nMany works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable »\, the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras\, representations of Virasoro algebras\, the theory of conformal blocks). However\, for Liouville Theory this was not done at the mathematical level by algebraic methods. \nI’ll explain how to combine probabilistic\, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks\, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure\, which is viewed as the space of fields\, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space. \nThis is joint work with A. Kupiainen\, R. Rhodes and V. Vargas. URL:https://cmsa.fas.harvard.edu/event/10-21-2021-interdisciplinary-science-seminar/ LOCATION:MA CATEGORIES:Interdisciplinary Science Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211022T093000 DTEND;TZID=America/New_York:20211022T103000 DTSTAMP:20260510T020118 CREATED:20240213T105511Z LAST-MODIFIED:20240304T101145Z UID:10002466-1634895000-1634898600@cmsa.fas.harvard.edu SUMMARY:The Large D Limit of Einstein’s Equations DESCRIPTION:Abstract: 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. URL:https://cmsa.fas.harvard.edu/event/10-22-2021-general-relativity-seminar/ LOCATION:MA CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211022T093000 DTEND;TZID=America/New_York:20211022T103000 DTSTAMP:20260510T020118 CREATED:20240214T073722Z LAST-MODIFIED:20240301T111559Z UID:10002564-1634895000-1634898600@cmsa.fas.harvard.edu SUMMARY:Wall-crossing from Higgs bundles to vortices DESCRIPTION:Speaker: Du Pei \nTitle: Wall-crossing from Higgs bundles to vortices \nAbstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk\, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices. URL:https://cmsa.fas.harvard.edu/event/10-22-2021-member-seminar/ LOCATION:MA CATEGORIES:Member Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211025T130000 DTEND;TZID=America/New_York:20211025T140000 DTSTAMP:20260510T020118 CREATED:20240214T093259Z LAST-MODIFIED:20240301T082800Z UID:10002633-1635166800-1635170400@cmsa.fas.harvard.edu SUMMARY:Exploring the Holographic Swampland DESCRIPTION:Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space\, such as LVS in type IIB or the DGKT flux vacua in type IIA\, the dual moduli conformal dimensions reduce to fixed values – in a certain sense\, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer\, for reasons we do not understand. URL:https://cmsa.fas.harvard.edu/event/10-25-2021-swampland-seminar/ LOCATION:MA CATEGORIES:Swampland Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211026T090000 DTEND;TZID=America/New_York:20211026T100000 DTSTAMP:20260510T020118 CREATED:20240213T113529Z LAST-MODIFIED:20240304T101126Z UID:10002507-1635238800-1635242400@cmsa.fas.harvard.edu SUMMARY:The n-queens problem DESCRIPTION:Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash. URL:https://cmsa.fas.harvard.edu/event/10-26-2021-combinatorics-physics-and-probability-seminar/ LOCATION:MA CATEGORIES:Combinatorics Physics and Probability END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211026T130000 DTEND;TZID=America/New_York:20211026T140000 DTSTAMP:20260510T020118 CREATED:20240214T062643Z LAST-MODIFIED:20240304T063155Z UID:10002549-1635253200-1635256800@cmsa.fas.harvard.edu SUMMARY:On singular Hilbert schemes of points DESCRIPTION:Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points. URL:https://cmsa.fas.harvard.edu/event/on-singular-hilbert-schemes-of-points/ LOCATION:MA CATEGORIES:Algebraic Geometry in String Theory Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211027T093000 DTEND;TZID=America/New_York:20211027T103000 DTSTAMP:20260510T020118 CREATED:20240214T043101Z LAST-MODIFIED:20240502T151724Z UID:10002529-1635327000-1635330600@cmsa.fas.harvard.edu SUMMARY:Anisotropy\, biased pairing theory and applications DESCRIPTION:Speaker: Karim 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. URL:https://cmsa.fas.harvard.edu/event/anisotropy-biased-pairing-theory-and-applications/ LOCATION:MA CATEGORIES:Colloquium ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.27.21.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211027T140000 DTEND;TZID=America/New_York:20211027T150000 DTSTAMP:20260510T020118 CREATED:20240214T093929Z LAST-MODIFIED:20240517T193105Z UID:10002641-1635343200-1635346800@cmsa.fas.harvard.edu SUMMARY:Why explain mathematics to computers? DESCRIPTION:Speaker: Patrick Massot\, Laboratoire de Mathématiques d’Orsay and CNRS \nTitle: Why explain mathematics to computers? \nAbstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like\, what kind of things it teaches us\, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics\, and I won’t assume any prior knowledge about formalization. URL:https://cmsa.fas.harvard.edu/event/10-27-2021-new-technologies-in-mathematics-seminar/ LOCATION:MA CATEGORIES:New Technologies in Mathematics Seminar ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.27.21.png END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211028T093000 DTEND;TZID=America/New_York:20211028T103000 DTSTAMP:20260510T020118 CREATED:20240213T112817Z LAST-MODIFIED:20240304T102039Z UID:10002500-1635413400-1635417000@cmsa.fas.harvard.edu SUMMARY:The classical interior of charged black holes with AdS asymptotics DESCRIPTION:Abstract: 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. URL:https://cmsa.fas.harvard.edu/event/10-28-2021-general-relativity-seminar/ LOCATION:MA CATEGORIES:General Relativity Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211028T130000 DTEND;TZID=America/New_York:20211028T143000 DTSTAMP:20260510T020118 CREATED:20240213T112644Z LAST-MODIFIED:20240304T084647Z UID:10002498-1635426000-1635431400@cmsa.fas.harvard.edu SUMMARY:Drivers of Morphological Complexity DESCRIPTION:Abstract: During development\, organisms interact with their natural habitats while undergoing morphological changes\, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria\, a basal animal lineage that includes sea anemones\, corals\, hydras\, and jellyfish\, offers unique insight into the development and evolution of morphological complexity.  In my talk\, I will introduce our research on “ethology of morphogenesis\,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels\, opening new perspectives about the design principle of soft-bodied animals. In addition\, I will discuss a fascinating feature of cnidarian biology. For humans\, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly\, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule. \nReferences\nAnniek Stokkermans\, Aditi Chakrabarti\, Ling Wang\, Prachiti Moghe\, Kaushikaram Subramanian\, Petrus Steenbergen\, Gregor Mönke\, Takashi Hiiragi\, Robert Prevedel\, L. Mahadevan\, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976 \nIkmi A\, Steenbergen P\, Anzo M\, McMullen M\, Stokkermans M\, Ellington L\, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensis. Nature communications\, Sept 02; 11:4399 \nHe S\, Del Viso F\, Chen C\, Ikmi A\, Kroesen A\, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensis. Science\, Vol. 361\, Issue 6409\, pp. 1377-1380.\nIkmi A\, McKinney SA\, Delventhal KM\, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensis. Nature communications. Nov 24; 5:5486. URL:https://cmsa.fas.harvard.edu/event/drivers-of-morphological-complexity/ LOCATION:MA CATEGORIES:Active Matter Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211028T184500 DTEND;TZID=America/New_York:20211028T204500 DTSTAMP:20260510T020118 CREATED:20240301T104157Z LAST-MODIFIED:20240305T104709Z UID:10002894-1635446700-1635453900@cmsa.fas.harvard.edu SUMMARY:ARCH: Know What Your Machine Doesn’t Know DESCRIPTION:Speaker: Jie Yang\, Delft University of Technology \nTitle: ARCH: Know What Your Machine Doesn’t Know \nAbstract: Despite their impressive performance\, machine learning systems remain prohibitively unreliable in safety-\, trust-\, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk\, I will present our ongoing work on ARCH\, a knowledge-driven\, human-centered\, and reasoning-based tool\, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic\, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk\, I will present several applications in which ARCH is currently being developed and tested\, including health\, finance\, and smart buildings. URL:https://cmsa.fas.harvard.edu/event/10-28-2021-interdisciplinary-science-seminar/ LOCATION:MA CATEGORIES:Interdisciplinary Science Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211029T093000 DTEND;TZID=America/New_York:20211029T103000 DTSTAMP:20260510T020118 CREATED:20240214T073521Z LAST-MODIFIED:20240301T111455Z UID:10002563-1635499800-1635503400@cmsa.fas.harvard.edu SUMMARY:The complex Monge-Ampere equation in K\”ahler geometry DESCRIPTION:Speaker: Freid Tong \nTitle: The complex Monge-Ampere equation in Kahler geometry \nAbstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry\, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk\, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry\, with a particular focus on the a priori C^0 estimates and their various applications. In the end\, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations\, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations. URL:https://cmsa.fas.harvard.edu/event/10-29-2021-member-seminar/ LOCATION:MA CATEGORIES:Member Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211029T120000 DTEND;TZID=America/New_York:20211029T130000 DTSTAMP:20260510T020118 CREATED:20240214T102641Z LAST-MODIFIED:20240301T091452Z UID:10002670-1635508800-1635512400@cmsa.fas.harvard.edu SUMMARY:Anomaly resolution via decomposition DESCRIPTION:Speaker: Eric Sharpe (Virginia Tech) \nTitle: Anomaly resolution via decomposition \nAbstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly\, for our purposes\, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition\, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups\, of which the extensions of [X/G] are examples.  After a review of decomposition\, we will see that decomposition implies that in (1+1) dimensions\, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G. URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics/ LOCATION:Virtual CATEGORIES:Quantum Matter END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211029T120000 DTEND;TZID=America/New_York:20211029T130000 DTSTAMP:20260510T020118 CREATED:20240301T091725Z LAST-MODIFIED:20240301T091725Z UID:10002890-1635508800-1635512400@cmsa.fas.harvard.edu SUMMARY:Integrability and chaos of 1+1d chiral edge states DESCRIPTION:Speaker: Biao Lian (Princeton) \nTitle: Integrability and chaos of 1+1d chiral edge states \nAbstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states\, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states\, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions\, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models\, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly\, I will talk about the analytical and numerical study of the 4/3 FQH edge theory\, which shows unusual behavior in its integrability. URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics-2/ LOCATION:MA CATEGORIES:Quantum Matter END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211101T130000 DTEND;TZID=America/New_York:20211101T140000 DTSTAMP:20260510T020118 CREATED:20240214T092956Z LAST-MODIFIED:20240301T081324Z UID:10002631-1635771600-1635775200@cmsa.fas.harvard.edu SUMMARY:Bubble instability of mIIA on AdS_4 x S^6 DESCRIPTION:Speaker: Pieter Bomans\, Princeton \nTitle: Bubble instability of mIIA on AdS_4 x S^6 \nAbstract: Recently\, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore\, they are stable against a variety of non-perturbative decay channels. Hence\, at this point\, they represent a serious challenge to the AdS swampland conjecture. In my talk\, I will review in detail the construction of these vacua as well as introduce a new decay channel\, ultimately sealing their fate as being unstable. URL:https://cmsa.fas.harvard.edu/event/11-1-2021-swampland-seminar/ LOCATION:MA CATEGORIES:Swampland Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/New_York:20211102T093000 DTEND;TZID=America/New_York:20211102T103000 DTSTAMP:20260510T020118 CREATED:20240213T062436Z LAST-MODIFIED:20240213T062436Z UID:10002107-1635845400-1635849000@cmsa.fas.harvard.edu SUMMARY:Counting invariant curves on a Calabi-Yau threefold with an involution DESCRIPTION:Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk\, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g\,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g\,h) which are conjectured to be equivalent\, one in terms of a version of PT theory\, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases\, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface\, the specialization of n_beta(g\,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco. URL:https://cmsa.fas.harvard.edu/event/counting-invariant-curves-on-a-calabi-yau-threefold-with-an-involution/ LOCATION:MA CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Jim-Bryan_poster_3Nov2021.png END:VEVENT END:VCALENDAR