Seminars Sorted by Series

This talk is going to be an extended and more technical version of my brief public lecture https://www.ias.edu/ideas/2017/arora-zemel-machine-learningI will present some of the basic ideas of machine learning, focusing on the mathematical...

We will give a brief overview of the classical topics, problems and results in Algebraic Combinatorics. Emerging from the representation theory of $S_n$ and $GL_n$, they took a life on their own via the theory of symmetric functions and Young...

Symplectic Geometry and its dynamics originated from classical mechanics as the geometry of physical phase space, in particular from celestial mechanics, and one of the most driving questions is up to today that of stability for such systems. One of...

This talk will survey ideas surrounding a conjecture in number theory about the structure of class groups of number fields. Each number field has associated to it a finite abelian group, the class group, and as long ago as Gauss, deep questions...

Classical and quantum Hamiltonian actions of reductive groups, respectively, give rise to ubiquitous families of commuting flows and of commutative rings of operators. I will explain how a construction of Ngô (from the proof of the Fundamental Lemma...

Last semester I gave a talk that was a 1-hour condensation of undergrad machine learning. https://www.ias.edu/video/membsem/2017/1127-SanjeevArora . This semester's talk will be a 1-hour treatment of some research directions in theoretical machine...

This talk will be an introduction to the methods used in the study of spectral properties of Schroedinger operators with a potential defined via the action of an ergodic transformation. Open problems relating to Lyapunov exponents over a skew shift...

I will survey what is known about the construction of (the building blocks of) representations of p-adic groups, mention recent developments, and explain some of the concepts underlying all constructions. In particular, I will introduce filtrations...

We will hear from two passionate creators of successful mentoring programs in math for high school kids in educationally challenged environments. They will give back-to-back talks about their experiences and educational insights.
Rajiv Gandhi: "From...

Complexity of the geometry, randomness of the potential, and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization: a phenomenon of confinement of waves, or eigenfunctions, to a small...

There is a remarkable parallel between the theory of Coxeter groups (think of the symmetric group Sn or the dihedral group Dn) and matroids (think of your favorite graph or vector configuration). After giving an overview of the similarity, I will...

Three fundamental factors determine the quality of a statistical learning algorithm: expressiveness, optimization and generalization. The classic strategy for handling these factors is relatively well understood. In contrast, the radically different...

In this talk I will survey recent advances on the existence theory of minimal hypersurfaces from the variational point of view. I will discuss what we know, what we do not know and point to future directions. This is based on joint works with Andre...

In a series of works with Laszlo Szekelyhidi Jr. we pointed out an unusual analogy between two problems in rather distant areas: a long standing conjecture of Onsager in the theory of turbulence and a (less known) critical regularity problem in...

In this talk I will present a survey of some of the famous results and examples in the classical theory of minimal and constant mean curvature surfaces in R^3. The first examples of minimal surfaces were found by Euler (catenoid) around 1741...

A key challenge in homogeneous dynamics is understanding the action of higher rank diagonal groups on homogenous spaces. While actions of rank one diagonal groups have a lot of flexibility, a phenomena used already by Artin to engineer orbits of...

Computation of the stable homotopy groups of spheres is a long-standing open problem in algebraic topology. I will describe how chromatic homotopy theory uses localization of categories, analogous to localization for rings and modules, to split this...

In this talk we explain how billiard dynamics can be used to relate a symplectic isoperimetric-type conjecture by Viterbo with an 80-years old open conjecture by Mahler regarding the volume product of convex bodies. The talk is based on a joint work...

Based on the Lagarias-Odlyzko effectivization of the Chebotarev density theorem, Kumar Murty gave an effective version of the Sato-Tate conjecture for an elliptic curve conditional on the analytic continuation and the Riemann hypothesis for all the...

Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all...

The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed netflow at each vertex. We will discuss a family of subdivisions of flow polytopes and explain how they give rise to a family...

We show that every complete Riemannian manifold of finite volume contains a complete embedded minimal hypersurface of finite volume. This is a joint work with Gregory Chambers.

How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown cyclic shifts? This simple problem has surprisingly broad applications, in fields from aircraft radar imaging to structural biology with the...

Quantum modular forms were defined in 2010 by Zagier; they are somewhat analogous to ordinary modular forms, but they are defined on the rational numbers Q as opposed to the upper half complex plane H, and they transform in Q under the action of the...

Positive geometries are real semialgebraic sets inside complex varieties characterized by the existence of a meromorphic top-form called the canonical form. The defining property of positive geometries and their canonical forms is that the residue...

I will discuss some geometric inequalities that hold on Riemannian 2-disks and 2-spheres.

For example, I will prove that on any Riemannian 2-sphere there M exist at least three simple periodic geodesics of length at most 20d, where d is the...

The goal is to describe how techniques from symplectic dynamics can be used to study orbit travel in three dimensions, for systems like the restricted 3-body problem from celestial mechanics. The pseudo-holomorphic curve theory initiated by Hofer...

In the early 1930's, the Ergodic theorems of von Neumann and Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms, and the natural question was born: is ergodicity the "general case" among conservative dynamical systems? Oxtoby and Ulam...

Invariant theory is a fundamental subject in mathematics, and is potentially applicable whenever there is symmetry at hand (group actions). In recent years, new problems and conjectures inspired by complexity have come to light. In this talk, I will...

Deligne's "Weil II" paper includes a far-reaching conjecture to the effect that for a smooth variety on a finite field of characteristic p, for any prime l distinct from p, l-adic representations of the etale fundamental group do not occur in...

Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear group. We will discuss both continuous and discrete concavity property of Schur polynomials. There will be one theorem and eight conjectures...