
Speaker: Alejandro PovedaTitle: On compactness phenomenaVenue: CMSA Room G10Member Seminar Speaker: Alejandro Poveda Title: On compactness phenomena Abstract: In this presentation I shall be preoccupied with compactness phenomena in set theory. Compactness is the phenomenon by which the local properties of a mathematical structure determine its global behavior. This phenomenon is intrinsic to the very architecture of the mathematical universe and manifests to us in a cornucopia of forms. Over the past fifty years, the study of compactness phenomena has been a cornerstone of research in set theory. This talk will present recent discoveries regarding compactness principles, spanning classical themes like the tree property and stationary reflection, while also forging novel connections with other topics, such as Woodin’s HOD Conjecture. 

Speaker: Juven WangTitle: Open Problems in Physics and Novel Solutions from MathVenue: CMSA Room G10Member Seminar Speaker: Juven Wang Title: Open Problems in Physics and Novel Solutions from Math Abstract: (1) How do neutrinos obtain tiny mass and oscillate between e, \mu, \tau three flavors? What consists of Dark Matter? What causes leptogenesis and baryogenesis? (2) Why the Parity Symmetry is violated in the weak interaction? How do we quantum mechanically regularize and numerically simulate the Standard Model (chiral fermion/gauge theory) on the lattice in 3+1 spacetime dimensions? (3) Strong CP problem: Why is the neutron electric dipole moment nearly zero and QCD respects the CP = T symmetry? (4) Family/Generation problem: Why are there three families/generations of quarks and leptons? In my talk, I will sketch and propose novel solutions to these challenging open problems in… 

Speaker: Samy JelassiTitle: An introduction to mixture of experts in deep learningVenue: CMSA Room G10Member Seminar Speaker: Samy Jelassi Title: An introduction to mixture of experts in deep learning Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. MixtureofExperts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By doing so, the parameter count is decoupled from the compute per example leading to very large, but efficient models. In this talk, I will review the concept of mixture of experts, provide a basic description of the Switch Transformers model, characterize some of their behaviors and conclude by highlighting some open problems in the field. This talk is mainly based on the following papers: https://arxiv.org/pdf/2101.03961.pdf, https://arxiv.org/pdf/2209.01667.pdf . 

Speaker: Aghil AlaeeTitle: A quasilocal mass in general relativityVenue: CMSA Room G10Member Seminar Speaker: Aghil Alaee Title: A quasilocal mass in general relativity Abstract: 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 gaugeindependent quasilocal mass and energy with respect to the Minkowski spacetime, and show its relation to the BrownYork HamiltonJacobi analysis. A quasilocal proof of the positivity, based on spacetime harmonic functions, is given for admissible closed spacelike 2surfaces which enclose an initial data set satisfying the dominant energy condition. Rigidity is also established in that vanishing energy implies that the 2surface arises from an embedding into… 

Speaker: Zi Yang KangTitle: Deformations of LandauGinzburg models and their fibersVenue: CMSA Room G10Member Seminar Speaker: Zi Yang Kang Title: Deformations of LandauGinzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a LandauGinzburg model. Broadly, a LandauGinzburg model is quasiprojective 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 LandauGinzburg 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… 

Speaker: Iacopo BrivioTitle: Extension of pluricanonical forms in positive and mixed characteristicsVenue: CMSA Room G10Member Seminar Speaker: Iacopo Brivio (CMSA) Title: Extension of pluricanonical forms in positive and mixed characteristics Abstract: 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… 

Speaker: Daniel KapecTitle: Black Holes as Quantum SystemsVenue: CMSA Room G10Member Seminar Speaker: Daniel Kapec (CMSA) Title: Black Holes as Quantum Systems Abstract: 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 lowtemperature 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 lowtemperature thermodynamics of the Kerr black hole that resolves many of the old… 

Speaker: Puskar MondalTitle: On the Breakdown of Einstein’s GravityVenue: CMSA Room G10Member Seminar Speaker: Puskar Mondal (CMSA) Title: On the Breakdown of Einstein’s Gravity Abstract: It is important to understand under which conditions, the solutions of nonlinear 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. 

Speaker: Benjamin McKennaTitle: Random matrices and large deviationsVenue: CMSA Room G10Member Seminar Speaker: Benjamin McKenna Title: Random matrices and large deviations Abstract: 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. 

Speaker: Kai XuTitle: Moduli of vector bundles on curve and semiorthogonal decompositionVenue: CMSA Room G10Member Seminar Speaker: Kai Xu (CMSA) Title: Moduli of vector bundles on curve and semiorthogonal decomposition Abstract: 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 BorelWeilBott theory for loop groups, derived SchurWeyl duality for current groups and derived Θstratification. 

Speaker: Chuck DoranTitle: Modularity of LandauGinzburg ModelsVenue: Common Room, CMSAMember Seminar Speaker: Chuck Doran Title: Modularity of LandauGinzburg Models Abstract: 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 (MoriMukai classification). What does Mirror Symmetry have to say about such classifications? By studying the LandauGinzburg models mirror to smooth Fano threefolds we can transform the MoriMukai 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). 

Speaker: Sunghyuk ParkTitle: Quantum UVIR map and curve counts in skeinsVenue: CMSA Room G10Member Seminar Speaker: Sunghyuk Park Title: Quantum UVIR map and curve counts in skeins Abstract: Quantum UVIR map (a.k.a. qnonabelianization 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. In this talk, I will discuss how quantum UVIR map can be generalized to a map between HOMFLYPT skein modules, using skeinvalued curve counts of Ekholm and Shende. 

Speaker: Gabriel WongTitle: Quantum information and extended topological quantum field theoryVenue: CMSA Room G10Member Seminar Speaker: Gabriel Wong Title: Quantum information and extended topological quantum field theory Abstract: 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… 

Speaker: Aghil AlaeeTitle: Toroidal Positive Mass TheoremVenue: CMSA Room G10Member Seminar Speaker: Aghil Alaee Title: Toroidal Positive Mass Theorem Abstract: 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. 

Speaker: Freid TongTitle: On complete CalabiYau metrics and some related MongeAmpere equationsVenue: CMSA Room G10Member Seminar Speaker: Freid Tong Title: On complete CalabiYau metrics and some related MongeAmpere equations Abstract: We will give a basic introduction to constructions for complete CalabiYau metrics. A systematic approach to construct such metrics using PDE methods was proposed in the work of TianYau 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. 

Speaker: Puskar MondalTitle: Recent progress on coupled EinsteinYangMills dynamicsVenue: Common Room, CMSAMember Seminar Speaker: Puskar Mondal Title: Recent progress on coupled EinsteinYangMills dynamics Abstract: I will discuss my recent work with prof. S.T. Yau on EinsteinYangMills theory. I’ll discuss the main ideas behind the stability of the Minkowski and Milne space time under coupled gaugegravity perturbations. Construction of the gauge invariant energies that control the suitable norms of the physical degrees of freedom in a doublenull framework play an important role. I’ll sketch how the special structure of the Einstein and YangMills nonlinearities play a crucial role in obtaining the stability result of nonexpanding spacetimes in particular AF spacetimes. 

Speaker: Changji XuTitle: Spectral gap and twopoint functions in spin glassesVenue: CMSA Room G10Member Seminar Speaker: Changji Xu Title: Spectral gap and twopoint functions in spin glasses Abstract: 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 twopoint functions in spin glasses models. 

Speaker: Faidra MonachouTitle: Optimal Dynamic Allocation: Simplicity through Information DesignVenue: CMSA Room G10Member Seminar Speaker: Faidra Monachou Title: Optimal Dynamic Allocation: Simplicity through Information Design Abstract: We study dynamic nonmonetary markets where objects are allocated to unitdemand 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 directrevelation 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… 

Speaker: Jue LiuTitle: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifoldsVenue: CMSA Room G10Member Seminar Speaker: Jue Liu Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds Abstract: 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 BrownYork 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… 

Speaker: Max WiesnerTitle: Quantum Gravity constraints beyond asymptotic regimesVenue: CMSA Room G10Member Seminar Speaker: Max Wiesner Title: Quantum Gravity constraints beyond asymptotic regimes Abstract: 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 lowenergy 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 nontrivial 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… 