Title: Fourier uniformity of multiplicative functions

Abstract: The Fourier uniformity conjecture seeks tounderstand what multiplicative functions can have large Fourier coefficients onmany short intervals. We will discuss recent progress on this problem andexplain its connection with the distribution of prime numbers and with othercentral problems about the behaviour of multiplicative functions, such as theChowla and Sarnak conjectures.

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Speaker: Maryna Viazovska (EPFL)

Title: Random lattices with symmetries
Abstract: What is the densest lattice sphere packing in the d-dimensional Euclidean space? In this talk, we will investigate this question as the dimension goes to infinity, and we will focus on the lower bounds for the best packing density, or in other words, on the existence results. We will give a historical overview of the lower bounds proved by H. Minkowski, E. Hlawka, C. L. Siegel, C. A. Rogers, and more recently by S. Vance and A. Venkatesh. In the final part of the lecture, we will present recent work done in collaboration with V. Serban and N. Gargava on the moments of the number of lattice points in a bounded set for random lattices constructed from a number field.

Mathematics Hall, room 417 from 4:30 – 5:30pm

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Speaker: Professor Ezra Getzler (Northwestern University)

Title: Generalizing Lie theory to higher dimensions – the De Rham theorem on simplices and cubes

Abstract: There is a generalization of Lie theory from Lie algebras to differential graded Lie algebras. Ordinary Lie theory involves first order ordinary differential equations. Higher Lie theory may be understood as a non-linear generalization of the de Rham theorem on simplicial complexes (in Dupont’s formulation), as against graphs. In this talk, we present an alternate approach to this theory, using the more elementary de Rham theorem on cubical complexes.
Along the way, we will need an interesting relationship between cubical and simplicial complexes, which has recently become better known due to its use in Lurie’s theory of straightening for infinity categories.

Mathematics Hall, room 407 from 4:30 – 5:30pm

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The Graduate School of Arts and Sciences joins the greater Columbia community in mourning the loss of Henry Pinkham, former dean, chair, and professor for nearly 50 years, who passed away suddenly in late June 2023.

A memorial service for Professor Pinkham is planned for Friday, November 17, 2023, from 11:00 am – 2:00 pm at Faculty House.

RSVPs should be sent to sophie.pinkham@gmail.com.

For more information, please visit: https://www.gsas.columbia.edu/content/memoriam-henry-c-pinkham-former-dean-gsas

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Special Lecture Series

Speaker: Professor Nikita Nekrasov (Simons Center for Geometry and Physics and Columbia)

The Count of Instantons

Abstract: Graduate level introduction to modern mathematical physics with the emphasis on the geometry and physics of quantum gauge theory and its connections to string theory.  We shall zoom in on a corner of the theory especially suitable for exploring non-perturbative aspects of gauge and string theory: the instanton contributions. Using a combination of methods from algebraic geometry, topology, representation theory and probability theory we shall derive a series of identities obeyed by generating functions of integrals over instanton moduli spaces, and discuss their symplectic, quantum, isomonodromic, and, more generally, representation-theoretic significance.

Quantum and classical integrable systems, both finite and infinite-dimensional ones, will be a recurring cast of characters, along with the other (qq-) characters.

First lecture: Friday, September 15, 2023

Fridays at 1:30pm until 3pm (except for the following dates: 10/6 , 10/20/, 11/3, 11/17, 11/24, 12/1-12/8 (TBD), and 12/15)

Room 520, Mathematics Hall

2990 Broadway (117th Street)

Flyer

Notes

Lecture notes: Not split per lecture will be updated as course continues

Lecture recording

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Simon Brendle, a professor of mathematics, has been awarded the Breakthrough Prize. The annual prize was founded in 2012 by sponsors Sergey Brin, Priscilla Chan and Mark Zuckerberg, Julia and Yuri Milner, and Anne Wojcicki, and touts itself as the world’s largest international science prize. It comes with a $3 million award. Professor Brendle was recognized for “a series of remarkable leaps in differential geometry, a field that uses the tools of calculus to study curves, surfaces and spaces. Many of his results concern the shape of surfaces, as well as manifolds in higher dimensions than those we experience in everyday life.”

“We’re thrilled to see Professor Brendle’s work recognized in such a public way. His ongoing research on differential geometry and nonlinear partial differential equations is of vital importance for the field, and he is a treasured member of the Columbia community,” said Johan de Jong, the chair of the mathematics department.

For more information, please visit Professor Simon Brendle Wins Breakthrough Prize | Columbia News

Columbia’s Instagram post

Breakthrough Reception 2023 photos by Eileen Barroso for Columbia Research Teams

Photo credits: Photographer Eileen Barroso

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The Fall 2023 Minerva Foundation Lectures will take place on Wednesdays at 2:45 p.m. in room 507. Professor Sergiu Klainerman (Princeton University), will deliver a series of lectures titled:

Columbia Lectures on the Stability of Kerr

The main goals of these lectures are:
1. Provide a comprehensive introduction to the proof of the nonlinear stability of slowly rotating Kerr black holes established recently in the sequence of works [Kl-Sz:Kerr], [GKS-2022], [Kl-Sz:GCM1], [Kl-Sz:GCM2] and [Shen], and briefed in [Kl-Sz:review].

2. Discuss the geometric formalism based on non-integrable null horizontal structures used in these works. Derive the main Teukolsky and generalized Regge- Wheeler equations. These follow the material 1 of Part 1 in [GKS-2022].

3. Discuss the proof of the basic hyperbolic estimates, Morawetz and rp-weighted, following Part 2 of [GKS-2022].

4. Discuss open problems related to these topics.

First lecture: Wednesday, September 6, 2023

Meeting on Wednesdays at 2:45 p.m.

Room 507, Mathematics Hall

2990 Broadway (117th Street)

Flyer

Notes

Notes Part II

Notes Part III

Lecture recording

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The Fall 2023 Samuel Eilenberg Lectures will take place on Tuesdays at 4:10 p.m. in room 520. Professor Laurent Fargues (Institut de Mathématiques de Jussieu-Paris), will deliver a series of lectures titled:

Some new geometric structures in the Langlands program

Abstract: Starting from Harris-Taylor and my PHD work on the geometric realization of the local Langlands correspondences to my recent joint work with Scholze, I will explain the new geometric structures that have emerged in the Langlands program. For the first time, ideas of the geometric Langlands program have been imported into the classical Langlands program in characteristic zero. To give life to those ideas we developed with Scholze some new geometry, following my work with Fontaine where we began to give a meaning to the idea of an holomorphic function of the variable p where p is a prime number. I will explain this new geometry and its applications to the Langlands program.”

First lecture: Tuesday, September 12, 2023

Tuesdays at 4:10pm

Room 520, Mathematics Hall

2990 Broadway (117th Street)

Flyer

Notes

Lecture recording

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COMAP is pleased to announce the results of the 39th annual Mathematical Contest in Modeling (MCM). This year, 11,296 teams representing institutions from twenty-one countries/regions participated in the contest. Twenty-Two teams from the following institutions were designated as OUTSTANDING WINNERS.

The first team consisting of Maksym Bondarenko, Philip M. Yan, and Caden Lin, received the title of Outstanding Winner and was awarded the MAA award.

To view the seven outstanding winners of the MCM (A) Problem, please visit this link.

The second team consisting of Steven Sofos DiSilvio, Anthony Ozerov, and Leon Zhou, received the title of Outstanding Winner and was awarded the INFORMS and the MAA award.

To view the twelve outstanding winner of the MCM (C) Problem, please visit this link. 

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