We are pleased to welcome Professor Avi Wigderson (Institute for Advanced Study, Princeton) for a lecture to be held on:
Thursday 2 July from 15:30 to 17:00
in Auditorium BCH 2201
Title: Optimization, Complexity and Math (or, can we prove P!=NP by gradient descent?)
Abstract:
This talk aims to summarize a project I was involved in during the past decade, with the hope of explaining our most complete understanding so far, as well as challenges and open problems. The main messages of this project are summarized below; I plan to describe, through examples, many of the concepts they refer to, and the evolution of ideas leading to them. No special background is assumed.
We extend the most basic tools of convex optimization in Euclidean space to a far more general setting of Riemannian manifolds that arise from the symmetries of noncommutative groups. We develop first-order and second-order algorithms, and analyze their performance in general. Invariant theory, which studies such group actions, plays an essential role in this development. The focus on symmetries exposes old and reveals new relations between the application problems below.
These algorithms give exponential (or better) improvements in run-time for solving algorithmic many problems across CS, Math and Physics. In particular, these include problems in algebra (e.g. testing rational identities in non-commutative variables), in analysis (testing the feasibility and tightness of Brascamp-Lieb inequalities), in quantum information theory (to the quantum marginals problem), in algebraic geometry (to computing Kronecker coefficients), in computational complexity (to derandomizing new special cases of the PIT problem) and in optimization (to testing membership in large, implicitly described polytopes).
Based on joint works with Zeyuan Allen-Zhu, Peter Burgisser, Cole Franks, Ankit Garg, Leonid Gurvits, Pavel Hrubes, Yuanzhi Li, Visu Makam, Rafael Oliveira and Michael Walter.
The event will be followed by an apéritif.
Please register using the link below by Wednesday 24 June 2026.
REGISTER HERE : Lecture Prof. Avi Wigderson (IAS, Princeton) – Fill in form
