Walter D. Neumann, 1946-2024

It is with deep sadness and heavy hearts that we inform you of the death of Prof. Walter Neumann, who passed away yesterday. Heartfelt condolences are extended to his family, friends, and loved ones.

Walter received his PhD at Bonn University in 1969 and became a Barnard Professor in 2000. He was a member of the European Academy of Sciences (elected 2002) and a Fellow of the American Mathematical Society since 2012. He worked in geometry and topology and especially on low dimensional topology, for example on hyperbolic 3-manifolds and geometric group theory.

A website with a cv, autobiographical account of his early life, a celebration written by Alan W. Reid, a list of his PhD students, and a gallery of pictures can be found here:

https://celebratio.org/Neumann_WD/cover/948/

A Zoom memorial will be held in his honor for family, friends, and colleagues; additional details will be announced in the near future.

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Title: The stability-compactness method and qualitative properties of nonlinear elliptic PDEs

Speaker: Henri Berestycki (University of Maryland, College Park & EHESS, Paris)

Date, Time, Location: Wed. October 16th @ 4:30 PM in 520 Math Hall

Abstract: Nonlinear elliptic equations describe the stationary states of numerous systems in physics, biology and medicine. Qualitative properties such as monotonicity, symmetry, stability or uniqueness are essential features of their study. In this talk, I will present a new general framework to approach this kind of questions, focusing on uniqueness. It rests on decomposing the domain into one region with a certain compactness feature and another supporting a form of spectral stability. This approach has proved to be unexpectedly versatile and in fact encompasses past works on the subject such as the general moving plane method originating in the study of minimal surfaces by Alexandrov. The results concern positive solutions of nonlinear elliptic PDEs in general unbounded domains with Dirichlet boundary conditions and for various types of reaction terms. This represents a series of joint works with Cole Graham and with Cole Graham and Jun-Cheng Wei.

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Title: Matrix Rigidity

Speaker: Josh Alman (Columbia CS)

Date, Time, Location: Wed. Sept 25 @ 4:30 PM in 520 Math Hall

Abstract: A matrix is called rigid if one must change many of its entries before it becomes a low-rank matrix. Leslie Valiant introduced the notion in 1977 as a tool to prove lower bounds on the number of arithmetic operations needed to compute linear transformations like the discrete Fourier transform. Since then, many connections have been demonstrated between matrix rigidity and other topics in the theory of computation.

Unfortunately, proving that matrices of interest are rigid has shown to be a major challenge. In fact, it remains an open problem to prove that any explicit family of matrices is rigid. By contrast, it is known that a random matrix is rigid with high probability.

In this talk, I’ll give a brief overview of matrix rigidity and its uses in computer science. I’ll then discuss some recent results, including proofs that matrices like Hadamard and Fourier matrices, which were previously conjectured to be rigid, are in fact not rigid. The talk will not assume the audience has a background in computer science.

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Please join us in congratulating Professor Richard Hamilton on being awarded the Chinese Basic Science Lifetime Award in Mathematics by the International Congress of Basic Science.  (more)

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In a new edition of “Office Hours”, Columbia News interviews Ritt Assistant Professor Amadou Bah about his experience in “Teaching Math on the Global Stage“.

Read the full article at https://news.columbia.edu/news/teaching-math-global-stage.

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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.

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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