New Technologies in Mathematics Seminar Speaker: Riccardo Zecchina (Bocconi University) Title: Local learning needs dendrites Abstract: I will present a learning scheme for recurrent networks in which nonlinear dendrites enable learning by generating and stabilizing task-relevant attractors within a representation manifold. The scheme is local in space and time and matches the performance of backpropagation […]
Member Seminar Speaker: Yiqi Liu Title: An Introduction to Statistical Inference for Partially Identified Models Abstract: Classical statistical inference often relies on asymptotic approximations that are valid for each fixed data-generating process but may fail to hold uniformly over a class of relevant distributions. Starting with the familiar t-test, I will illustrate why this distinction […]
Geometry and Mathematical Physics Seminar Speaker: Spiro Karigiannis, University of Waterloo Title: A tale of two Lie groups Abstract: The classical Lie group SO(4) is well-known to possess a very rich structure, relating in several ways to complex Euclidean spaces. This structure can be used to construct the classical twistor space Z over an oriented […]
AI for the Working Mathematician Speaker: Lauren Williams, Harvard Title: First Proof Batch 3: Mathematicians putting AI to the test Abstract: First Proof is an initiative that aims to obtain a nuanced, objective assessment about the capabilities of large language models to prove specified mathematical statements. I will report on the results of First Proof's third […]
AI for the Working Mathematician Speaker: Jordan Ellenberg, University of Wisconsin-Madison Title: Large Hypercubes Abstract: I'll talk about this paper: Bruhat intervals that are large hypercubes <arxiv.org/abs/2601.01235> in which we use a tool from Google, AlphaEvolve, to discover unexpected combinatorial structures inside the symmetric group (to be precise, a large hypercube in the Bruhat order.) I'll […]
Geometry and Mathematical Physics Seminar Speaker: John Alexander Cruz Morales, Universidad Nacional de Colombia Title: Towards a Hodge theoretic mirror symmetry for punctured surfaces Abstract: In their 1992 paper, “Ising Model and N=2 Supersymmetric Theories,” Cecotti and Vafa asserted that a certain hyperelliptic configuration space of chiral fields is mirror to the Ising model. Today, this statement can […]
Colloquium Speaker: Subhabrata Sen, Harvard Statistics Title: Spectral Methods for signal recovery in multi-modal problems Abstract: Motivated by multi-modal estimation, we will study a multi-view spiked random matrix model in which several noisy matrix observations contain correlated spikes. We will introduce a new spectral method for signal recovery in this setting and characterize the behavior […]
CMSA Special Seminar Speaker: Michael Brenner Title: A physical interpretation of recent singularity theorems Abstract: We present a physical interpretation of recent mathematical proofs (Córdoba and Martínez-Zoroa; Buckmaster and Apogee; OpenAI) for singularity formation in nonlinear partial differential equations with smooth forcing. In our formulation, singularity formation is driven by a forward in time process whereby […]
Member Seminar Speaker: Aaron Landesman Title: Painlevé VI: the search for canonical representations Abstract: In 1902, Painlevé classified second order differential equations whose only movable singularities are poles, thereby obtaining the six Painlevé equations. Algebraic solutions to Painlevé's sixth equation correspond to canonical triples of 2 by 2 complex matrices. One can alternatively view these […]
Geometry and Mathematical Physics Seminar Speaker: Tobias Ekholm, Uppsala Title: Skein valued curve counts and associatives Abstract: We consider Lagrangians in the cotangent bundle of a 3-manifold that give branch covers the 0-section. A circle bundle over the cotangent bundle that degenerates over the Lagrangian gives an A_n-fibration over the base 3-manifold. We equip this A_n […]
AI for the Working Mathematician Speaker: Harold Williams, USC Title: An Informal Introduction to Formal Proofs Abstract: In this talk we will give an introduction to Lean, a programming language adapted to expressing and verifying proofs. Lean and its flagship library, mathlib, have been the focus of a dedicated user community for about a decade, […]
Colloquium Speaker: Mehran Kardar, MIT Title: Life on a Noisy Seascape: Extinction, Growth, and Diversity Abstract: Populations and communities rarely evolve in static environments; their fitness landscapes fluctuate across space and time, forming what may be called a noisy seascape. This talk examines how such variability modifies classical models of population dynamics and community stability. Beginning from the […]