Seminars Sorted by Series

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In this work, joint with A. Mohammadi, we try to classify all the discrete transitive actions on the vertices of a Bruhat-Tits Building over a local field of characteristic zero. There are lots of such actions in the case of Bruhat-Tits tree, i.e...

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...