Title: Malle’s conjecture over function fields

Speaker: Aaron Landesman (Harvard)

Date, Time, Location: Monday, Jan. 26th @4:30 – 5:30PM in Math Hall 520

Abstract:

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Starting Tues. Jan 27th, the Spring 2026 Samuel Eilenberg Lectures
will take place on Tuesdays at 2:40 – 3:55 PM
in Room 520, Mathematics Hall.

Professor Robert Bryant will deliver a series of lectures titled
Non-classical PDE in Differential Geometry.

Flyer

Many systems of partial differential equations that arise naturally in differential geometry do not fit easily into the usual paradigms of determined elliptic, hyperbolic, or parabolic systems, and the analysis of such systems has tended to be somewhat ad hoc. A systematic approach to the analysis of such systems, pioneered by Élie Cartan and Erich Kähler and brought to maturity by Masatake Kuranishi (among others), has been available for about 70 years, but the theory is not well-known, which hampers its application in many problems of current interest.

In this lecture series, I will start by discussing a number of interesting problems in differential geometry, such as prescribed curvature or holonomy, isometric deformation and related problems, curvature-homogeneity, calibrated geometry and calibrations, an approach to cluster algebras due to Kontsevich, etc. I will then discuss some tools needed to approach these problems, such as Cartan’s generalizations of Lie’s fundamental theorems about Lie groups, Cartan characters, and the modern theory of characteristics.

The emphasis will be on understanding the theory through application to interesting examples. Some time will be spent explaining how symbolic calculation software, such as MAPLE, can be used effectively in the analysis of such problems. Familiarity with basic differential geometry and classical PDE will be assumed, but not much beyond this.

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Title: Yang-Mills, probability, and stochastic PDE

Speaker: Sky Cao (MIT)

Date, Time, Location: Friday, Jan. 30th @3 – 4PM in Math Hall 520

Abstract:

Originating in physics, Yang-Mills theory has shaped many areas of modern mathematics. In my talk, I will present Yang-Mills theory in the context of probability, highlighting central questions and recent advances. In particular, I will discuss the role of stochastic partial differential equations (SPDEs) in these developments and survey some of the recent progress in this field.

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Title: The reasonable effectiveness of physics in mathematics

Speaker: Sheldon Katz (University of Illinois at Urbana-Champaign)

Date, Time, Location: Thursday, Nov. 13th @3PM – 4PM in Math Hall 520

Abstract:

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Congratulations to Professor Robert Friedman for being inducted into the 2026 class of Fellows of the American Mathematical Society.

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Please join us on Wednesday, November 12th
for the distinguished Ellis R. Kolchin Memorial Lecture.

Haruzo Hida (UCLA) will give a special talk titled
“Adjoint L-value and the Tate conjecture”

Time & Location:
Wednesday, November 12 @ 4:30pm
Mathematics Hall, Room 520
2990 Broadway
New York, N.Y. 10027

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Congratulations to Professor Mehtaab Sawhney for being named a recipient of the 2025 Packard Fellowships for Science and Engineering. read more »

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Congratulations to Professor Duong Phong on his appointment as Davies Chair of Mathematics.

Previous holders of the Davies Chair include Lipman Bers, Masatake Kuranishi, and Richard Hamilton.

Professor Phong joined Columbia in 1978. He has made fundamental contributions to many areas of mathematics, including harmonic analysis, partial differential equations, complex differential geometry, and mathematical physics. His contributions include his work with Charles Fefferman on subelliptic operators; his work with Elias Stein on singular integrals and Radon transforms; and his recent work on a-priori estimates for the complex Monge-Ampère equation.

Professor Phong has received many awards and distinctions for his work, including the André Aisenstadt Chair of the Université de Montréal (2000), the Bergman Prize of the American Mathematical Society (2009), and the Frontiers of Science Award (2024). He was elected a member of the American Academy of Arts and Sciences (2013) and the United States National Academy of Sciences (2024).

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A memorial for Professor Richard Streit Hamilton will be held on Sunday, September 28th. Please complete this form to attend by 9/14. Find the schedule of events for “Remembering the Life and Work of Richard Streit Hamilton” here.

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