Seminars Sorted by Series

In his study of the Baum-Connes conjecture, Vincent Lafforgue was lead to study Banach space representations of SL(n>2,F) (for F a local field) which are not by isometries but by operators of slowly growing norm. Classical tools to study unitary...

The classical Lagrange and Markov spectra encode the features of certain Diophantine approximations problems. The first systematic study of these spectra was done by Markov in 1880. Since then, these objects attracted the attention of several...

The purpose of the talk is to explain how additive combinatorics plays a role in recent work on the dimension of self-affine measures generated by maps satisfying a diophantine condition. Under low-entropy or separation assumptions, this problem is...

We show that closed negatively curved locally symmetric spaces are characterized among nearby Riemannian manifolds by the Lyapunov exponents of their geodesic flow along periodic orbits. Our methods extend to locally characterize the geodesic flows...

This talk will give a detailed introduction to the proof of Zimmer's conjecture made in recent work with Brown and Hurtado. The talk will be independent of Monday's member seminar, but I will not repeat history and motivation. I will begin by (re...

Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one...

The "linearization" technique is a powerful method in homogeneous dynamics to control the time a unipotent orbit spends in the vicinity of a closed homogeneous subset. This method relies on the polynomial nature of a unipotent flow and does not...

Let $X \subset \R^N$ be a Borel set, $\mu$ a Borel probability measure on $X$ and $T:X \to X$ a Lipschitz and injective map. Fix $k \in \N$ greater than the (Hausdorff) dimension of $X$ and assume that the set of $p$-periodic points has dimension...

We will discuss results connecting the titular objects on infinite graphs, including some known results by Varopoulos and Coulhon and Saloff-Coste and some new resutls.

I'll try to explain what we currently understand about the theoretical power of quantum computers, in a way that's accessible to a general math and physics audience. In particular, I'll demolish the popularly-held belief that quantum computing means...

British intelligence agency MI6 in 1939 recruited English mathematician Alan Turing, portrayed by Benedict Cumberbatch, to decipher Nazi codes including Enigma codes. Turing, assisted by Joan Clarke, portrayed by Keira Knightley, worked to analyze...

Both of these talks will be useful preparation for Helmut Hofer's up coming mini-course on polyfold theory on April 4th and 5th

Both of these talks will be useful preparation for Helmut Hofer's up coming mini-course on polyfold theory on April 4th and 5th.

In recent research it has become clear that there are fascinating connections between constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment in terms of Quillen...

The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics where sets are used to parametrize collections of objects without...

A "proof assistant" is a software package comprising a validity checker for proofs in a particular logic, accompanied by semi-decision procedures called "tactics" that assist the mathematician in filling in the easy parts of the proofs. I will...

Schedule: https://johnnash.princeton.edu/nashcelebration/

The main purpose of the talk is to describe an approach for the estimate of averages over orbits of certain functions on the space of lattices. These estimates play a crucial role in the study of the distribution of values at integral points of...

In this talk I will give an overview of joint work with M. Rapoport and T. Yang on the construction of generating series whose coefficients are the classes of special divisors and 0-cycles on the arithmetic surfaces attached to Shimura curves. These...

We discuss the Kadaira-Spencer gauge theory (or BCOV theory) on Calabi-Yau geometry. We explain Givental's loop space formalism at cochain level which leads to a degenerate BV theory on Calabi-Yau manifolds. Homotopic BV quantization together with a...

Recent imaging techniques for acquiring and processing microscopic data, combined with computational models and simulations, are leading to a mechanistic understanding of the development of patterns and forms in plants. This presentation will focus...

This is a report on joint work in progress with T. Kragh, wherein we prove that a closed exact Lagrangian in a cotangent bundle is simply homotopy equivalent to the base. I will explain the two main ingredients of the proof: (i) realising the...

Let a circle act symplectically on a closed symplectic manifold $M$. If the action is Hamiltonian, we can pass to the reduced space; moreover, the fixed set largely determines the cohomology and Chern classes of $M$. In particular, symplectic circle...

An intriguing primitive representation, "expand-and-sparsify", appears in the olfactory system of the fly and the sensory systems of several other organisms. It maps an input vector to a much higher-dimensional sparse representation, using a random...

Twenty years ago, a link was discovered between the neurotransmitter dopamine and the computational framework of reinforcement learning. Since then, it has become well established that dopamine release reflects a reward prediction error, a surprise...

This talk presents evidence that humans learn complex functions by harnessing compositionality: complex structure is decomposed into simpler building blocks. I formalize this idea in the framework of Bayesian nonparametric regression using a grammar...

People learn in fast and flexible ways that elude the best artificial neural networks. Once a person learns how to “dax,” they can effortlessly understand how to “dax twice” or “dax vigorously” thanks to their compositional skills. In this talk, we...