Seminars Sorted by Series

The sum-of-squares (SOS) hierarchy (due to Shor'85, Parrilo'00, and Lasserre'00) is a widely-studied meta-algorithm for (non-convex) polynomial optimization that has its roots in Hilbert's 17th problem about non-negative polynomials.SOS plays an...

Combinatorial geometry is a field that studies combinatorial problems that involve some simple geometric objects/notions, such as: lines, points, distances, collinearity. While such problems are often easy to state, some of them are very difficult...

Four years ago, Cachazo, He and Yuan found a system of algebraic equations, now named the "scattering equations", that effectively encoded the kinematics of massless particles in such a way that the scattering amplitudes, the quantities of physical...

Locally symmetric spaces are a class of Riemannian manifolds which play a special role in number theory. In this talk, I will introduce these spaces through example, and show some of their unusual properties from the point of view of both analysis...

We introduce the notion of a "crystallographic sphere packing," which generalizes the classical Apollonian circle packing. Tools from arithmetic groups, hyperbolic geometry, and dynamics are used to show that, on one hand, there is an infinite zoo...

In this talk, I will discuss the behavior of hard-core lattice particle systems at high fugacities. I will first present a collection of models in which the high fugacity phase can be understood by expanding in powers of the inverse of the fugacity...

Decomposition theorem for perverse sheaves on algebraic varieties, proved by Beilinson-Bernstein-Deligne-Gabber, is one of the most important and useful theorems in the contemporary mathematics. By the Riemann-Hilbert correspondence, we may regard...

The definition of the Kauffman bracket skein algebra of an oriented surface was originally motivated by the Jones polynomial invariant of knots and links in space, and a representation of the skein algebra features in Witten's topological quantum...

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...