During the 2023–24 academic year, the CMSA will be hosting a Colloquium series, organized by Alejandro Poveda and Kai Xu. It will take place from 4:30 – 5:30 pm (Eastern Time) in Room G10, CMSA, 20 Garden Street. All CMSA postdocs/members are required to attend the weekly CMSA Colloquium series as well as the weekly CMSA Members’ Seminars. The schedule will be updated as talks are confirmed.

CMSA COVID-19 Policies



  • March 09, 2022 09:30 AM
Speaker: Yen-Hsi Richard Tsai
Title: Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
Venue: Virtual

Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension…

  • March 02, 2022 09:30 AM
Speaker: Richard Kenyon
Title: Dimers and webs
Venue: Virtual

Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.

  • February 23, 2022 01:22 PM
Speaker: Bartek Czech
Title: Holographic Cone of Average Entropies and Universality of Black Holes
Venue: Virtual

Abstract:  In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by…

  • February 23, 2022 09:30 AM
Speaker: Bartek Czech
Title: 2/23/2022 CMSA Colloquium
Venue: Virtual

During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. Spring 2022 Date Speaker Title/Abstract 1/26/2022 Samir Mathur (Ohio State University) Title: The black hole information paradox Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected…

  • February 16, 2022 09:30 AM
Speaker: Takuro Mochizuki
Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles
Venue: Virtual

Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied. In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • February 16, 2022 09:30 AM
Speaker: Takuro Mochizuki (Kyoto University)
Title: 2/16/2022 CMSA Colloquium
Venue: Virtual

Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles Abstract: In 1960’s, Narasimhan and Seshadri discovered the equivalence between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then, many interesting generalizations have been studied. In this talk, we would like to review a stream in the study of such correspondences for Higgs bundles, integrable connections, $D$-modules and periodic monopoles.

  • February 08, 2022 09:30 AM
Speaker: Wenbin Yan
Title: CMSA Colloquium
Venue: Virtual

During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. Spring 2022 Date Speaker Title/Abstract 1/26/2022 Samir Mathur (Ohio State University) Title: The black hole information paradox Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected…

  • February 08, 2022 04:12 PM
Speaker: Wenbin Yan
Title: Tetrahedron instantons and M-theory indices
Venue: Virtual

Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.

  • February 02, 2022 09:30 AM
Speaker: Adam Smith
Title: Learning and inference from sensitive data
Venue: Virtual

Abstract: Consider an agency holding a large database of sensitive personal information—say,  medical records, census survey answers, web searches, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. I will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically, why such models must sometimes memorize training data points nearly completely. On the more positive side, I will present differential privacy, a rigorous definition of privacy in statistical databases that is now widely studied, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical…

  • January 26, 2022 09:30 AM
Speaker: Samir Mathur
Title: CMSA Colloquium
Venue: Virtual

During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. Spring 2022 Date Speaker Title/Abstract 1/26/2022 Samir Mathur (Ohio State University) Title: The black hole information paradox Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected…

  • January 26, 2022 09:30 AM
Speaker: Samir Mathur
Title: The black hole information paradox
Venue: Virtual

Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown, using some theorems from quantum information theory, that these extrapolations were incorrect, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines, with…

  • December 21, 2021 09:30 AM
Speaker:
Title: Colloquium 2021–22
Venue: Virtual

During the 2021–22 academic year, the CMSA will be hosting a Colloquium, organized by Du Pei, Changji Xu, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. Spring 2022 Date Speaker Title/Abstract 1/26/2022 Samir Mathur (Ohio State University) Title: The black hole information paradox Abstract: In 1975, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997, it was observed that black holes in string theory did not have the form expected…

  • December 15, 2021 09:30 AM
Speaker: Constantin Teleman
Title: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system
Venue: The Kapustin-Rozanski-Saulina "2-category" of a holomorphic integrable system
  • December 08, 2021 09:30 AM
Speaker: Maria Chudnovsky
Title: Induced subgraphs and tree decompositions
Venue: Virtual
  • December 01, 2021 09:30 AM
Speaker: Richard Wentworth
Title: The Hitchin connection for parabolic G-bundles
Venue: Virtual
  • November 17, 2021 09:30 AM
Speaker: Andrea Brini
Title: Curve counting on surfaces and topological strings
Venue: Virtual
  • November 10, 2021 09:30 AM
Speaker: Peter Keevash
Title: Hypergraph decompositions and their applications
Venue: Virtual
  • November 03, 2021 09:30 AM
Speaker: Tamas Hausel
Title: Hitchin map as spectrum of equivariant cohomology
Venue: Virtual
  • October 27, 2021 03:12 PM
Speaker: Karim Adiprasito
Title: Anisotropy, biased pairing theory and applications
Venue: Virtual

Abstract: 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. In 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…

  • October 20, 2021 01:10 PM
Speaker: Peng Shan
Title: Categorification and applications
Venue: Virtual

Abstract: I will give a survey of the program of categorification for quantum groups, some of its recent development and applications to representation theory.