Home » Articles posted by Administrative Coordinator Added on March 13, 2026 by Administrative CoordinatorJoint Distinguished Interdisciplinary and Applied Mathematics and Mathematics Colloquium
Title: AI-Driven Mathematical Discovery: Singularities, Algorithms, and Beyond
Speaker: Javier Gómez-Serrano (Brown University)
Date, Time, Location: Wednesday, March 25th @4:30 PM – 5:30 PM in Math Hall 520
Abstract:
Machine learning is transforming mathematical discovery, enabling advances on longstanding open problems. This talk explores two complementary approaches illustrating different paradigms for AI and mathematics. On the one hand, I will present a systematic discovery of unstable singularities in multi-dimensional partial differential equations. While most numerical methods historically found only stable singularities, we discover families of unstable singularities requiring infinitely precise initial conditions. Combining curated machine learning architectures with high-precision optimization and mathematical analysis, we achieve in some cases near machine precision, meeting requirements for rigorous computer-assisted proofs. On the other, I will discuss AlphaEvolve, a general-purpose evolutionary coding agent that uses large language models to autonomously discover old and new mathematical constructions and potentially go beyond them. AlphaEvolve tackles a wide variety of problems across analysis, geometry, combinatorics, and number theory. This illustrates how general-purpose AI systems can systematically successfully explore broad mathematical landscapes at an unprecedented speed, leading us to do mathematics at scale. Together, these examples reveal complementary roles for machine learning and mathematics in the future: deep, precision-focused small models for specific problems versus broad, systematic exploration across domains via large models.
 Print this pageAdded on February 27, 2026 by Administrative CoordinatorStarting 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.
Print this pageAdded on February 20, 2026 by Administrative CoordinatorTitle: Can AI systems produce interesting proofs?
Speaker: Mohammed Abouzaid (Stanford)
Date, Time, Location: Thursday, Feb. 26th @4:30 PM – 5:30 PM in Math Hall 520
Abstract:
We recently released a set of 10 mathematical statements in arxiv:2602.05192, with known ibut unpublished short human proofs (about 5 pages), and attempted to ascertain how far AI systems can go in autonomously proving them. I will discuss why I think this exercise is interesting, what the outcome was from different systems, and some preliminary lessons from the results.
Print this pageAdded on January 26, 2026 by Administrative CoordinatorTitle: Malle’s conjecture over function fields
Speaker: Aaron Landesman (Harvard)
Date, Time, Location: Monday, Feb. 9th @4:30 – 5:30PM in Math Hall 520
Abstract:
The inverse Galois problem, a foundational question in number theory, asks whether every finite group $G$ can be realized as the Galois group of a field extension of the rational numbers. Malle’s conjecture is a refined version of the inverse Galois problem which predicts the asymptotic number of such extensions. In joint work with Ishan Levy, we prove a version of Malle’s conjecture, computing the asymptotic growth of the number of Galois $G$ extensions of $\mathbb F_q(t)$, for $q$ sufficiently large and relatively prime to $|G|$. We use tools from algebraic geometry to relate this conjecture to a question in topology about the cohomology of certain Hurwitz spaces. We then complete the proof by solving the topological question using techniques from homotopy theory.
Print this pageAdded on January 17, 2026 by Administrative CoordinatorSpeaker: Denis Nesterov (ETH Zurich)
Title: Compactifications and Degenerations
Date, Time, Location: Friday, Feb. 6th @3 – 4PM in Math Hall 520
Abstract: I will discuss a universal structure that appears in the compactification of spaces parametrizing points, maps, and vector bundles associated with a complex variety. It gives rise to numerous interesting correspondences between seemingly different geometries, shedding light on Hilbert schemes, Hurwitz spaces, and Gieseker moduli spaces of stable sheaves.
Print this pageAdded on January 17, 2026 by Administrative CoordinatorSpeaker: Lucas Mason-Brown (Texas)
Title: Unitary representations of semisimple Lie groups and conical symplectic singularities.
Date, Time, Location: Monday, Feb. 2nd @4:30 – 5:30PM in Math Hall 520
Abstract: One of the most fundamental unsolved problems in representation theory is to classify the set of irreducible unitary representations of a semisimple Lie group. In this talk, I will define a class of such representations coming from filtered quantizations of certain graded Poisson varieties. The representations I define are expected to form the “building blocks” of all unitary representations.
Print this pageAdded on January 16, 2026 by Administrative CoordinatorTitle: 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.
Print this pageAdded on November 06, 2025 by Administrative CoordinatorTitle: 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:
One of the reasons why theoretical physics has spawned the development of many surprising and deep ideas of mathematics in recent decades is the presence of symmetries in physics without an obvious counterpart in mathematics. In this talk, I focus on supersymmetry in physics, their topological twists, and applications to geometry and topology, including applications to relatively new but now mature areas of mathematics along with conjectural “applications in progress”.
Print this pageAdded on October 31, 2025 by Administrative CoordinatorCongratulations to Professor Robert Friedman for being inducted into the 2026 class of Fellows of the American Mathematical Society.
Print this pageAdded on October 15, 2025 by Administrative CoordinatorPlease 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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