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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231117T120000
DTEND;TZID=America/New_York:20231117T130000
DTSTAMP:20260630T050709
CREATED:20240227T113236Z
LAST-MODIFIED:20240227T113251Z
UID:10002879-1700222400-1700226000@cmsa.fas.harvard.edu
SUMMARY:A quasi-local mass in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Aghil Alaee \nTitle: A quasi-local mass in general relativity \nAbstract: One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime\, which can include a star\, black hole\, or galaxy. We define a new gauge-independent quasi-local mass and energy with respect to the Minkowski spacetime\, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity\, based on spacetime harmonic functions\, is given for admissible closed spacelike 2-surfaces which enclose an initial data set satisfying the dominant energy condition.  Rigidity is also established in that vanishing energy implies that the 2-surface arises from an embedding into Minkowski space\, and conversely\, the mass vanishes for any such surface. This is joint work with M. Khuri and S.T. Yau. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231103T120000
DTEND;TZID=America/New_York:20231103T130000
DTSTAMP:20260630T050709
CREATED:20240227T113702Z
LAST-MODIFIED:20240227T113702Z
UID:10002880-1699012800-1699016400@cmsa.fas.harvard.edu
SUMMARY:Deformations of Landau-Ginzburg models and their fibers
DESCRIPTION:Member Seminar \nSpeaker: Zi Yang Kang \nTitle: Deformations of Landau-Ginzburg models and their fibers \nAbstract: In mirror symmetry\, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly\, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w\, but not all such pairs correspond to Fano varieties under mirror symmetry\, so a very natural question to ask is: Which Landau-Ginzburg models are mirror to Fano varieties? In this talk\, I will discuss a cohomological characterization of mirrors of (semi-)Fano varieties\, focusing on the case of threefolds. I’ll discuss how this characterization relates to the deformation and Hodge theory of (Y\,w)\, and in particular\, how the classification of (semi-)Fano threefolds is related to questions about moduli spaces of lattice polarized K3 surfaces.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-11323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231027T120000
DTEND;TZID=America/New_York:20231027T130000
DTSTAMP:20260630T050709
CREATED:20240223T110834Z
LAST-MODIFIED:20240223T110834Z
UID:10002858-1698408000-1698411600@cmsa.fas.harvard.edu
SUMMARY:Extension of pluricanonical forms in positive and mixed characteristics
DESCRIPTION:Member Seminar \nSpeaker: Iacopo Brivio (CMSA) \nTitle: Extension of pluricanonical forms in positive and mixed characteristics \nAbstract: The geometry of a complex manifold $X$ is to a large extent determined by its pluricanonical forms\, i.e. global sections of $(\Omega^{\dim X}_X)^{\otimes m}$ for $m\geq 0$. A famous theorem of Siu states that when $X\to D$ is a smooth projective family of complex manifolds\, then every pluricanonical form on $X_0$ extends to the whole of $X$. Both this theorem and the tools used in its proof had a deep impact in higher dimensional birational geometry and moduli theory. In this talk I am going to give an overview of the extension problem for pluricanonical forms when $D$ is the spectrum of a positive or mixed characteristic discrete valuation ring. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231020T120000
DTEND;TZID=America/New_York:20231020T130000
DTSTAMP:20260630T050709
CREATED:20240223T110405Z
LAST-MODIFIED:20240223T110405Z
UID:10002856-1697803200-1697806800@cmsa.fas.harvard.edu
SUMMARY:Black Holes as Quantum Systems
DESCRIPTION:Member Seminar \nSpeaker: Daniel Kapec (CMSA) \nTitle: Black Holes as Quantum Systems \nAbstract: To an outside observer\, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless\, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance\, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy\, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-102023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231013T120000
DTEND;TZID=America/New_York:20231013T130000
DTSTAMP:20260630T050709
CREATED:20240223T105131Z
LAST-MODIFIED:20240223T105527Z
UID:10002852-1697198400-1697202000@cmsa.fas.harvard.edu
SUMMARY:On the Breakdown of Einstein's Gravity
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal (CMSA) \nTitle: On the Breakdown of Einstein’s Gravity \nAbstract: It is important to understand under which conditions\, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity\, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk\, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231006T120000
DTEND;TZID=America/New_York:20231006T130000
DTSTAMP:20260630T050709
CREATED:20240223T105546Z
LAST-MODIFIED:20240223T105621Z
UID:10002854-1696593600-1696597200@cmsa.fas.harvard.edu
SUMMARY:Random matrices and large deviations 
DESCRIPTION:Member Seminar \nSpeaker: Benjamin McKenna \nTitle: Random matrices and large deviations \nAbstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years\, classical results have been complemented by a variety of new ones\, in both the math and physics literatures\, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points\, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230929T120000
DTEND;TZID=America/New_York:20230929T130000
DTSTAMP:20260630T050709
CREATED:20240223T112516Z
LAST-MODIFIED:20240223T112516Z
UID:10002863-1695988800-1695992400@cmsa.fas.harvard.edu
SUMMARY:Moduli of vector bundles on curve and semiorthogonal decomposition
DESCRIPTION:Member Seminar \nSpeaker: Kai Xu (CMSA) \nTitle: Moduli of vector bundles on curve and semiorthogonal decomposition \nAbstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups\, derived Schur-Weyl duality for current groups and derived Θ-stratification. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92923/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230922T120000
DTEND;TZID=America/New_York:20230922T130000
DTSTAMP:20260630T050709
CREATED:20240223T112106Z
LAST-MODIFIED:20240223T112106Z
UID:10002861-1695384000-1695387600@cmsa.fas.harvard.edu
SUMMARY:Modularity of Landau-Ginzburg Models
DESCRIPTION:Member Seminar \nSpeaker: Chuck Doran \nTitle: Modularity of Landau-Ginzburg Models \nAbstract:  Fano varieties are the basic building blocks of algebraic varieties.  Smooth Fano varieties have been classified in dimensions one (the projective line)\, two (del Pezzo surfaces)\, and three (Mori-Mukai classification).  What does Mirror Symmetry have to say about such classifications?  By studying the Landau-Ginzburg models mirror to smooth Fano threefolds we can transform the Mori-Mukai classification into an effective uniruledness result for moduli spaces of certain K3 and abelian surfaces.  This is joint work with Andrew Harder\, Ludmil Katzarkov\, Mikhail Ovcharenko\, and Victor Przjalkowski (arXiv:2307.15607). \n  \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-92223/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230915T120000
DTEND;TZID=America/New_York:20230915T130000
DTSTAMP:20260630T050709
CREATED:20240223T112851Z
LAST-MODIFIED:20240223T112851Z
UID:10002864-1694779200-1694782800@cmsa.fas.harvard.edu
SUMMARY:Quantum UV-IR map and curve counts in skeins
DESCRIPTION:Member Seminar \nSpeaker: Sunghyuk Park \nTitle: Quantum UV-IR map and curve counts in skeins \nAbstract: Quantum UV-IR map (a.k.a. q-nonabelianization map)\, introduced by Neitzke and Yan\, is a map from UV line defects in a 4d N=2 theory of class S to those of the IR. Mathematically\, it can be described as a map between skein modules and is a close cousin of quantum trace map of Bonahon and Wong. \nIn this talk\, I will discuss how quantum UV-IR map can be generalized to a map between HOMFLYPT skein modules\, using skein-valued curve counts of Ekholm and Shende.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-91523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230515T120000
DTEND;TZID=America/New_York:20230515T130000
DTSTAMP:20260630T050709
CREATED:20230817T172120Z
LAST-MODIFIED:20240216T105142Z
UID:10001245-1684152000-1684155600@cmsa.fas.harvard.edu
SUMMARY:Quantum information and extended topological quantum field theory 
DESCRIPTION:Member Seminar \nSpeaker: Gabriel Wong \nTitle: Quantum information and extended topological quantum field theory \nAbstract: Recently\, ideas from quantum information theory have played an important role in condensed matter and quantum gravity research. Most of these applications focus on the entanglement structure of quantum states\, and the computation of entanglement measures such as entanglement entropy has been an essential part of the story. In this talk\, we will address some subtleties that arise when trying to define entanglement entropy in quantum field theory and quantum gravity. In particular\, we will explain why extended topological field theory provides a useful framework to define and compute entanglement entropy in a continuous system. Time permitting\, we will explain some recent applications of these ideas in low dimensional quantum gravity and to topological string theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-51523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230502T120000
DTEND;TZID=America/New_York:20230502T130000
DTSTAMP:20260630T050709
CREATED:20230817T171918Z
LAST-MODIFIED:20240118T085308Z
UID:10001244-1683028800-1683032400@cmsa.fas.harvard.edu
SUMMARY:Toroidal Positive Mass Theorem
DESCRIPTION:Member Seminar \nSpeaker: Aghil Alaee \nTitle: Toroidal Positive Mass Theorem \nAbstract: In this talk\, we review the positive mass conjecture in general relativity and prove a toroidal version of this conjecture in an asymptotically hyperbolic setting.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-5223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230425T120000
DTEND;TZID=America/New_York:20230425T130000
DTSTAMP:20260630T050709
CREATED:20230817T171725Z
LAST-MODIFIED:20240118T071815Z
UID:10001243-1682424000-1682427600@cmsa.fas.harvard.edu
SUMMARY:On complete Calabi-Yau metrics and some related Monge-Ampere equations
DESCRIPTION:Member Seminar \nSpeaker: Freid Tong \nTitle: On complete Calabi-Yau metrics and some related Monge-Ampere equations \nAbstract: We will give a basic introduction to constructions for complete Calabi-Yau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of Tian-Yau in the 90s and have attracted a lot of attention in recent years. I will discuss some joint work with B. Guo and T. Collins on a singular version of such a construction\, as well as some ongoing work with Prof. Yau on some related boundary value problems. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-42523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230418T120000
DTEND;TZID=America/New_York:20230418T130000
DTSTAMP:20260630T050709
CREATED:20230817T171352Z
LAST-MODIFIED:20240228T091907Z
UID:10001242-1681819200-1681822800@cmsa.fas.harvard.edu
SUMMARY:Recent progress on coupled Einstein-Yang-Mills dynamics
DESCRIPTION:Member Seminar \nSpeaker: Puskar Mondal \nTitle: Recent progress on coupled Einstein-Yang-Mills dynamics \nAbstract: I will discuss my recent work with prof. S.T. Yau on Einstein-Yang-Mills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gauge-gravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a double-null framework play an important role. I’ll sketch how the special structure of the Einstein and Yang-Mills nonlinearities play a crucial role in obtaining the stability result of non-expanding spacetimes in particular AF spacetimes.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-41823/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230411T120000
DTEND;TZID=America/New_York:20230411T130000
DTSTAMP:20260630T050709
CREATED:20230817T171211Z
LAST-MODIFIED:20240118T070619Z
UID:10001241-1681214400-1681218000@cmsa.fas.harvard.edu
SUMMARY:Spectral gap and two-point functions in spin glasses
DESCRIPTION:Member Seminar \nSpeaker: Changji Xu \nTitle: Spectral gap and two-point functions in spin glasses \nAbstract: Many have worked on spin glass models over the past 50 years\, including physicists\, mathematicians\, and computers. A question that arises is whether computers yield dependable simulation results. In this talk\, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-41123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230404T120000
DTEND;TZID=America/New_York:20230404T130000
DTSTAMP:20260630T050709
CREATED:20230817T171014Z
LAST-MODIFIED:20240228T092930Z
UID:10001240-1680609600-1680613200@cmsa.fas.harvard.edu
SUMMARY:Optimal Dynamic Allocation: Simplicity through Information Design
DESCRIPTION:Member Seminar \nSpeaker: Faidra Monachou \nTitle: Optimal Dynamic Allocation: Simplicity through Information Design \nAbstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object\, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e.\, the sum of values) and welfare (i.e.\, the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that\, when the social planner can design the information disclosed to the agents about the objects\, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation\, the information disclosed about each object is an interval containing the object quality\, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases\, these intervals become coarser\, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality\, in terms of the Lorenz order.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-4423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230328T120000
DTEND;TZID=America/New_York:20230328T130000
DTSTAMP:20260630T050709
CREATED:20230817T170827Z
LAST-MODIFIED:20240118T070227Z
UID:10001239-1680004800-1680008400@cmsa.fas.harvard.edu
SUMMARY:Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds
DESCRIPTION:Member Seminar \nSpeaker: Jue Liu \nTitle: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds \nAbstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity\, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass\, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass\, we define a new quasilocal mass using the Hamilton method. With this definition\, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture\, that is under what conditions there will be a static extension to the given Bartnik data.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-32823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230321T120000
DTEND;TZID=America/New_York:20230321T130000
DTSTAMP:20260630T050709
CREATED:20230817T170644Z
LAST-MODIFIED:20240118T070105Z
UID:10001238-1679400000-1679403600@cmsa.fas.harvard.edu
SUMMARY:Quantum Gravity constraints beyond asymptotic regimes
DESCRIPTION:Member Seminar \nSpeaker: Max Wiesner \nTitle: Quantum Gravity constraints beyond asymptotic regimes \nAbstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories\, that can be obtained as a low-energy approximation of quantum gravity\, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as\, e.g.\, weak coupling limits. Still\, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-32123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230314T120000
DTEND;TZID=America/New_York:20230314T130000
DTSTAMP:20260630T050709
CREATED:20230817T170402Z
LAST-MODIFIED:20240118T065025Z
UID:10001237-1678795200-1678798800@cmsa.fas.harvard.edu
SUMMARY:Randomized algorithms in combinatorics
DESCRIPTION:Member Seminar \nSpeaker: Michael Simkin \nTitle: Randomized algorithms in combinatorics \nAbstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly\, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples: \n\nEnumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?\nConstructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally\, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan\, Sah\, and Sawhney.\nThresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham\, Sah\, and Sawhney.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-31423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230307T120000
DTEND;TZID=America/New_York:20230307T130000
DTSTAMP:20260630T050709
CREATED:20230817T170153Z
LAST-MODIFIED:20240118T064352Z
UID:10001236-1678190400-1678194000@cmsa.fas.harvard.edu
SUMMARY:Categorical Symmetry of the Standard Model from Gravitational Anomaly 
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: Categorical Symmetry of the Standard Model from Gravitational Anomaly \nAbstract: In the Standard Model\, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.14765\, 2204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover\, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific\, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general\, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction\, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge\, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].
URL:https://cmsa.fas.harvard.edu/event/member-seminar-3723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230302T120000
DTEND;TZID=America/New_York:20230302T130000
DTSTAMP:20260630T050709
CREATED:20230817T165840Z
LAST-MODIFIED:20240118T052933Z
UID:10001235-1677758400-1677762000@cmsa.fas.harvard.edu
SUMMARY:New bounds on lattice covering volumes\, and nearly uniform covers
DESCRIPTION:Member Seminar \nSpeaker: Barak Weiss   \nTitle: New bounds on lattice covering volumes\, and nearly uniform covers \nAbstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK\, such that L+rK = R^n\, normalized by the covolume of L. Pairs (L\,K) with small covering volume correspond to efficient coverings of space by translates of K\, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem\, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE\, Hebrew University) and Oded Regev (CS\, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper\, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-3223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230221T120000
DTEND;TZID=America/New_York:20230221T130000
DTSTAMP:20260630T050709
CREATED:20230817T165641Z
LAST-MODIFIED:20240118T052804Z
UID:10001234-1676980800-1676984400@cmsa.fas.harvard.edu
SUMMARY:Hints of Flat Space Holography
DESCRIPTION:Member Seminar \nSpeaker: Dan Kapec \nTitle: Hints of Flat Space Holography \nAbstract: Despite our detailed understanding of holography in Anti-de Sitter space\, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space\, bulk gravitons produce a boundary stress tensor\, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-22123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230214T120000
DTEND;TZID=America/New_York:20230214T130000
DTSTAMP:20260630T050709
CREATED:20230817T165432Z
LAST-MODIFIED:20240228T094059Z
UID:10001233-1676376000-1676379600@cmsa.fas.harvard.edu
SUMMARY:Dynamics of active nematic defects on cones
DESCRIPTION:Member Seminar \nSpeaker: Farzan Vafa \nTitle: Dynamics of active nematic defects on cones \nAbstract: In the first part of the talk\, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge\, which in analogy to electrostatics\, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle\, which is determined by charged defects screening the effective apex charge: (i) for sharp cones\, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles\, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones\, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk\, we investigate the dynamics of an active nematic on a cone\, and via simulations find long-time circular orbits of either one or two flank defects\, with transitions between these states mediated by the apex via defect absorption\, emission\, or defect pair creation.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-21423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230207T120000
DTEND;TZID=America/New_York:20230207T130000
DTSTAMP:20260630T050709
CREATED:20230817T165237Z
LAST-MODIFIED:20240215T101240Z
UID:10001232-1675771200-1675774800@cmsa.fas.harvard.edu
SUMMARY:Motivic Geometry of Two-Loop Feynman Integrals
DESCRIPTION:Member Seminar \nSpeaker: Chuck Doran \nTitle: Motivic Geometry of Two-Loop Feynman Integrals \nAbstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves\, elliptic curves\, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular\, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves\, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly\, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230131T120000
DTEND;TZID=America/New_York:20230131T130000
DTSTAMP:20260630T050709
CREATED:20230817T164947Z
LAST-MODIFIED:20240118T033236Z
UID:10001231-1675166400-1675170000@cmsa.fas.harvard.edu
SUMMARY:AI and Theorem Proving
DESCRIPTION:Member Seminar \nSpeaker: Mike Douglas \nTitle: AI and Theorem Proving \nAbstract: We survey interactive theorem proving and the Lean theorem prover\, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-13123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221202T110000
DTEND;TZID=America/New_York:20221202T120000
DTSTAMP:20260630T050709
CREATED:20230817T164654Z
LAST-MODIFIED:20240229T111029Z
UID:10001230-1669978800-1669982400@cmsa.fas.harvard.edu
SUMMARY:Compactness and Anticompactness Principles in Set Theory
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Compactness and Anticompactness Principles in Set Theory \nAbstract: Several fundamental properties in Topology\, Algebra or Logic are expressed in terms of Compactness Principles.For instance\, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise\, we say that compactness fails. Loosely speaking\, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group\, a topological space\, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$\, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits\, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221118T110000
DTEND;TZID=America/New_York:20221118T120000
DTSTAMP:20260630T050709
CREATED:20230809T111725Z
LAST-MODIFIED:20240209T052933Z
UID:10001229-1668769200-1668772800@cmsa.fas.harvard.edu
SUMMARY:Light states in the interior of CY moduli spaces
DESCRIPTION:Member Seminar \nSpeaker: Damian van de Heisteeg \nTitle: Light states in the interior of CY moduli spaces \nAbstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction\, that is\, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points\, and find that they correspond to special points in the moduli space of the CY\, such as orbifold points and rank two attractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111822/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-11.18.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221111T110000
DTEND;TZID=America/New_York:20221111T120000
DTSTAMP:20260630T050709
CREATED:20230809T111328Z
LAST-MODIFIED:20240209T052938Z
UID:10001228-1668164400-1668168000@cmsa.fas.harvard.edu
SUMMARY:Quantum trace and length conjecture for hyperbolic knot
DESCRIPTION:Member Seminar \nSpeaker: Mauricio Romo \nTitle: Quantum trace and length conjecture for hyperbolic knot \nAbstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2\,C) Chern-Simons theory\, one can formulate a ‘length conjecture’ for the hyperbolic length of L.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221028T110000
DTEND;TZID=America/New_York:20221028T120000
DTSTAMP:20260630T050709
CREATED:20230809T110603Z
LAST-MODIFIED:20240301T080243Z
UID:10001227-1666954800-1666958400@cmsa.fas.harvard.edu
SUMMARY:Some non-concave dynamic optimization problems in finance
DESCRIPTION:Member Seminar \nSpeaker: Shuaijie Qian (Harvard CMSA) \nTitle: Some non-concave dynamic optimization problems in finance \nAbstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle\, and derives equivalent\, concave optimization problems whose value functions are still concave. In this talk\, I will present our recent work on some non-concave dynamic optimization problems\, where the concavification principle may not hold and the resulting value function is indeed non-concave. \nThe first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation\, where the average tax basis and the average mining cost serves as an approximation\, respectively. This approximation results in a non-concave value function\, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover\, the penalty method still works and converges to the value function. \nThe second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints\, which makes the concavification principle invalid\, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous\, we introduce a new definition of viscosity solution\, prove the corresponding comparison principle\, and show that a monotone\, stable\, and consistent finite difference scheme converges to the solution of the utility maximization problem. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-6/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221021T110000
DTEND;TZID=America/New_York:20221021T120000
DTSTAMP:20260630T050709
CREATED:20230809T110107Z
LAST-MODIFIED:20240301T080144Z
UID:10001226-1666350000-1666353600@cmsa.fas.harvard.edu
SUMMARY:Explicit Ramsey Graphs and Two Source Extractors
DESCRIPTION:Speaker: David Zuckerman\, Harvard CMSA/University of Texas at Austin \nTitle: Explicit Ramsey Graphs and Two Source Extractors \nAbstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N\, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-5/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221014T110000
DTEND;TZID=America/New_York:20221014T120000
DTSTAMP:20260630T050709
CREATED:20240214T103536Z
LAST-MODIFIED:20240301T081027Z
UID:10002676-1665745200-1665748800@cmsa.fas.harvard.edu
SUMMARY:Quantum magnet chains and Kashiwara crystals
DESCRIPTION:Speaker: Leonid Rybnikov\, Harvard CMSA/National Research University Higher School of Economics \nTitle: Quantum magnet chains and Kashiwara crystals \nAbstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are\, generally\, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely\, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves\, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically\, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva\, Joel Kamnitzer\, and Alex Weekes.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101422/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.14.22.png
END:VEVENT
END:VCALENDAR