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Periodic pencils of flat connections and their p-curvature

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Pavel Etingof (MIT) Title: Periodic pencils of flat connections and their p-curvature  A periodic pencil of flat connections on a smooth algebraic variety  is a linear family of flat connections  , where  are local coordinates on  and  are matrix-valued regular functions. A pencil is periodic if it is generically invariant under the shifts  up to isomorphism. I will […]

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Symmetry groups in infinite dimensions

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Lisa Carbone, Rutgers University Title: Symmetry groups in infinite dimensions Abstract: The study of many physical theories requires an understanding of symmetries of infinite dimensional Lie algebras. The construction of groups of automorphisms for infinite dimensional Lie algebras is challenging, but there is well established theory for the class of Kac-Moody algebras. A […]

Local complexity measures in modern parameterized function classes for supervised learning

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Elisenda Grigsby, Boston College Title: Local complexity measures in modern parameterized function classes for supervised learning Abstract: The parameter space for any fixed architecture of neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? For any fixed feedforward ReLU network architecture, it […]

Higher Vapnik–Chervonenkis theory

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Artem Chernikov, University of Maryland Title: Higher Vapnik–Chervonenkis theory Abstract: Finite VC-dimension, a combinatorial property of families of sets, was discovered simultaneously by Vapnik and Chervonenkis in probabilistic learning theory, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning, combinatorics, mathematical […]

The mathematics of evolution

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Martin Nowak (Harvard) Title: The mathematics of evolution Abstract: All living systems are guided by evolutionary dynamics. Evolution is a search process which occurs in populations of reproducing individuals. The three fundamental forces of evolution are mutation, selection and cooperation. I will present basic ideas in the mathematical description of evolutionary dynamics, including quasi-species theory, evolutionary […]

Mathematical Structures of Scattering Amplitudes

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Anastasia Volovich, Brown University Title: Mathematical Structures of Scattering Amplitudes Abstract: Planar N=4 Yang-Mills scattering amplitudes have been computed to very high loop order. They have many remarkable properties that have sparked interest from mathematicians working on combinatorics, algebraic geometry, and number theory. At the same time, several methods that have been developed […]

Computability on $\mathbb R$ and other continuum-size structures

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Russell Miller, CUNY Title: Computability on $\mathbb R$ and other continuum-size structures Abstract: We begin by recalling the notion of a computable function on the real numbers $\mathbb R$, developed independently by Gregorczyk and Lacombe over sixty years ago. Using this notion, we note that the real numbers that are themselves computable form […]

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Rational approximation and the AAA algorithm

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Nick Trefethen, Harvard University Title: Rational approximation and the AAA algorithm Approximation by rational functions used to be mainly a theoretical subject, but with the introduction of the AAA algorithm in 2018, it became computationally practical and indeed easy. The implications for what we can do numerically are enormous. This talk will outline […]

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AI in math and theoretical physics: Status and prospects

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Michael Douglas, Harvard CMSA Title: AI in math and theoretical physics: status and prospects Abstract: AI is making great progress and has the potential to change how we work in unprecedented ways. In this talk I will survey a few recent works which illustrate the state of the art, some from my own research, […]

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Large value estimates in number theory and computer science

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Larry Guth, MIT Title: Large value estimates in number theory and computer science Abstract: A large value estimate for a matrix M is a simple type of estimate in quantitative linear algebra. Estimates of this type appear in many parts of math, both pure and applied. One example is the large value problem for […]

The Toda Lattice as a Soliton Gas

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Amol Aggarwal, Columbia University Title: The Toda Lattice as a Soliton Gas Abstract: A basic tenet of integrable systems is that, under sufficiently irregular initial data, they can be thought of as dense collections of many solitons, or “soliton gases.” In this talk we focus on the Toda lattice, which is an archetypal example of […]

3-d Mirror Symmetry

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Colloquium Speaker: Ben Webster, University of Waterloo & Perimeter Institute Title: 3-d Mirror Symmetry Abstract: I'll give an introduction (or update, for those who've been introduced) to 3d mirror symmetry from the perspective of a mathematician.