Members’ Seminar

The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.

Previous seminars can be found here.

Spring 2021:

2/5/2021Itamar ShamirTitle: Boundary CFT and conformal anomalies

Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.
2/12/2021Louis FanTitle:  Joint distribution of Busemann functions in corner growth models

Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.
2/19/2021Daniel JunghansTitle: Control issues of the KKLT scenario in string theory

Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.
2/26/2021Tsung-Ju LeeTitle: SYZ fibrations and complex affine structures

Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

9:00pm ET
Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification

Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

9:00pm ET
Ryan ThorngrenTitle:  Symmetry protected topological phases, anomalies, and their classification 
Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

8:30am ET
Aghil AlaeeTitle:  Rich extra dimensions are hidden inside black holes

Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe. 
8:30am ET
Enno KeßlerTitle: Super Stable Maps of Genus Zero

Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.
4/9/2021Juven Wang

Title: Ultra Unification

Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
4/16/2021Sergiy VerstyukTitle: Deep learning methods for economics

Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.
4/23/2021Yifan WangTitle: Virtues of Defects in Quantum Field Theories

Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity. 
4/30/2021Yun ShiTitle: D-critical locus structure for local toric Calabi-Yau 3-fold

Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.
5/7/2021Thérèse Yingying WuTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2

Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.
5/14/2021Du Pei

Fall 2020:

9/11/2020Moran KorenTitle:  Observational Learning and Inefficiencies in Waitlists  

Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.
9/18/2020Michael DouglasTitle: A talk in two parts, on strings and on computers and math

Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.
9/25/2020Cancelled – Math Science Lecture
10/2/2020Cancelled – Math Science Lecture
10/9/2020Wai Tong (Louis) FanTitle: Stochastic PDE as scaling limits of interacting particle systems

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 discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I 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 new 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. Joint work with Rick Durrett.
10/16/2020Tianqi WuTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.
10/23/2020Changji XuTitle: Random Walk Among Bernoulli Obstacles

Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.
10/30/2020Michael SimkinTitle: The differential equation method in Banach spaces and the $n$-queens problem

Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.
11/6/2020Kenji KawaguchiTitle: Deep learning: theoretical results on optimization and mixup

Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.
11/13/2020Omri Ben-EliezerTitle: Sampling in an adversarial environment

Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply. 

We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.

Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.
11/20/2020Charles DoranTitle: The Calabi-Yau Geometry of Feynman Integrals

Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

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