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In Memoriam: Professor Henry C. Pinkham

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.

For more information, please visit:

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Special Lecture Series: The Count of Instantons

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)



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

Lecture recording

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Professor Simon Brendle Wins Breakthrough Prize

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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Fall 2023 Minerva Foundation Lectures

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)



Notes Part II

Notes Part III

Lecture recording

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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)



Lecture recording

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Columbia University Undergraduate Students Win the INFORMS Award & MAA Award

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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Congratulations to Professor Marcel F. Nutz named IMS Fellow

2023 IMS Fellow

Marcel F. Nutz, Professor, Columbia University, has been named Fellow of the Institute of Mathematical Statistics (IMS).  Dr. Nutz received the award for outstanding contributions to probability, in particular to optimal transport, stochastic analysis, and mathematical finance; and for dedicated service to the profession.

The designation of IMS Fellow has been a significant honor for over 85 years. Each Fellow is assessed by a committee of their peers and has demonstrated distinction in research or leadership that has profoundly influenced the field. Established in 1935, the Institute of Mathematical Statistics is a member organization that fosters the development and dissemination of the theory and applications of statistics and probability. The IMS has over 4,700 active members throughout the world. Approximately 10% of the current IMS membership has earned the status of fellowship. The announcement of the 2023 class of IMS Fellows can be viewed here.

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Incoming class of 2023

The incoming graduate class for 2023 has been announced. For a list of the new students, please visit the incoming class page.

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Will Sawin awarded Sloan Fellowship

Will Sawin, an Associate Professor in the Mathematics Department, was recently selected as a recipient for the prestigious Sloan Fellowship award. From the Sloan Research Fellowship website:

“The Sloan Research Fellowships seek to stimulate fundamental research by early-career scientists and scholars of outstanding promise. These two-year fellowships are awarded yearly to 126 researchers in recognition of distinguished performance and a unique potential to make substantial contributions to their field.”

For more information please visit:

To view all 2023 Sloan research fellows, please visit:

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April 19: Tomer Schlank

Speaker: Tomer Schlank (Hebrew University in Jerusalem)
Title:  Knots Invariants and Arithmetic Statistics.

Abstract: The Grothendieck school introduced \’etale topology to attach algebraic-topological invariants such as cohomology to varieties and schemes. Although the original motivations came from studying varieties over fields, interesting phenomena such as Artin–Verdier duality also arise when considering the spectra of integer rings in number fields and related schemes. A deep insight, due to B. Mazur, is that through the lens of \’etale topology, spectra of integer rings behave as 3-dimensional manifolds while prime ideals correspond to knots in these manifolds. This knots and primes analogy provides a dictionary between knot theory and number theory, giving some surprising analogies. For example, this theory relates the linking number to the Legendre symbol and the Alexander polynomial to Iwasawa theory.  In this talk, we shall start by describing some of the classical ideas in this theory. I shall then proceed by describing how via this theory, giving a random model on knots and links can be used to predict the statistical behavior of arithmetic functions. This is joint work with Ariel Davis.

Where: Mathematics Hall, room 520
When: Wednesday, April 19, 2023 at 04:30pm

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