Seminars Sorted by Series

A central problem in the theory of L-functions is to investigate their sizes on the critical line. The convexity bound, which follows from the Phragmen-Lindelof principle, is of little use in applications. Therefore much effort has been made to...

Abstract: The first two lectures will expand the panorama of research areas, motivations, problems and results in the scope of this workshop, highlighting many of the topics and lectures during this week. We will focus on one problem: the...

Abstract: The first two lectures will expand the panorama of research areas, motivations, problems and results in the scope of this workshop, highlighting many of the topics and lectures during this week. We will focus on one problem: the...

Abstract: Symmetries are a main source of unifying principles in mathematics and physics and groups are the appropriate mathematical concept for describing symmetries. Representation theory studies linear transformations in the presence of...

Abstract: An invariant is a function that remains unchanged under certain transformations. If an invariant has different values on two objects, then we have an easy proof that one object cannot be transformed into the other. In Invariant Theory one...

Abstract: We will give a gentle introduction to geometric invariant theory, which provides geometric and analytic tools to study problems in invariant theory. We will explain the basic tools and concepts and give many motivating examples. In the...

Abstract: In this second lecture, we will continue our gentle introduction. We will discuss some of the underlying geometry and introduce the associated moment polytopes. These are a rich class of convex polytopes that arise naturally in a variety...

Abstract: Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer...

Abstract: We wish to understand when a tensor s can be transformed into a tensor t by application of linear maps to its tensor legs (we then say s restricts to t). In the language of restrictions, the rank of a tensor t is given by the minimal size...

In 1967, J. Edmonds introduced the problem of computing the rank over the rational function field of an $n \times n$ matrix $M_1x_1 + \dotsb + M_mx_m$ whose entries are homogeneous linear polynomials in commuting variables $x_1, x_2, \dotsc, x_m$...

Abstract: We show some results from (classical commutative) Polynomial Identity Testing in which the results or the technical ingredients of the noncommutative rank algorithm presented in the preceding talk play an important role. These include...

Abstract: Many important problems in computational complexity can be rewritten in the language of invariant theory. Famous examples include the graph isomorphism problem, and the GCT approach to P vs NP. The focus of this talk will be to illustrate...

Abstract:This talk will describe some algorithmic challenges, relevant to this workshop, that arise in the context of the geometric complexity theory (GCT) approach to the fundamental lower bound and polynomial identity testing problems of...

Abstract: It has long been understood that endowing a convex body with a Riemannian metric derived from the Hessian of a convex function can be instrumental in controlling the convergence of flows (local algorithms) toward equilibrium. This is...

Abstract: Sometimes, functions that are non-convex in the Euclidean space turn out to be convex if one introduces a suitable metric on the space and redefines convexity with respect to the straight lines ("geodesics") induced by the metric. Such a...

Abstract: We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and...

Abstract: The Paulsen problem is a basic open problem in operator theory. We define a continuous version of the operator scaling algorithm to solve this problem. A key step is to show that the continuous operator scaling algorithm converges faster...

Abstract: Let P be a matrix property, e.g. having rank at most (or at least) k, being nilpotent, having no multiple eigenvalues, etc. We will survey some old and new results and problems on the maximal dimension of linear spaces of matrices having...

Abstract: The Quantum Permanent, the operator(explicitely) and polynomial(just for determinantal polynomials) Capacities were introduced by L.G. in 1999 on the DIMACS Matrix Scaling Workshop. The original motivation for the Quantum Permanent and the...

“Deep learning” refers to use of neural networks to solve learning problems, including “learning” hidden structures in large and complex data sets. The theory for this field is still in its infancy. Lately physical and biological scientists have...

In this introductory seminar I will cover the main machine learning techniques so-far adopted to study interacting quantum systems. I will first introduce the concept of neural-network quantum states [1], a representation of the many-body wave...

Understanding phenomena in systems of many interacting quantum particles, known as quantum many-body systems, is one of the most sought-after objectives in contemporary physics research. The challenge of simulating such systems lies in the extensive...

Please Note: The seminars are not open to the general public, but only to active researchers. Register here for this event: https://docs.google.com/forms/d/e/1FAIpQLScJ-BUVgJod6NGrreI26pedg8wGEyP… Abstract for talk #1: The affinity between...

Archives staff members will give a presentation on the history of the Institute and the School of Mathematics for members of the School of Math's special year on the Univalent Foundations of Mathematics. Following the presentation, group members...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

During August 2-13 there will be held a mini-workshop in Princeton that will bring together applied mathematicians and structural biologists.A tentative schedule is here: https://www.ias.edu/math/files/seminars/MiniWorkshopSchedule.pdf Every day...

The "P vs. NP" problem, formulated by computer theorists in the 1970s, quickly became a central outstanding problem of science and mathematics. In this talk I will attempt to describe its mathematical, scientific and philosophical content. I will...

This talk will give a brief outline of the algorithm, followed by technical details of the second combinatorial partitioning algorithm ("Split-or-Johnson" routine) required for the group theoretic recurrence. The technical material will be...

We review the theory of multiple Dirichlet series which are Dirichlet series in several complex variables having analytic continuation with finitely many polar divisors and satisfying a finite group of functional equations. Converse theorems state...

This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the...

Picard-Lefschetz theory studies algebraic varieties by induction on their dimension. It can be used to determine their topology, and in more modern terms their symplectic geometry. We will apply this theory to describe extra structure which appears...

Anabelian geometry techniques allow the construction of explicit universal spaces which capture birational properties of algebraic varieties. I will describe this theory and its applications (joint with F. Bogomolov).