Convexity Seminar

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Online Komlos converges to mean curvature flow

Speaker: Vlad Kobzar, The Ohio State University

Location: Warren Weaver Hall 1302

Date: Tuesday, April 14, 2026, 11 a.m.

Synopsis:

We establish a direct connection between combinatorial discrepancy minimization problems and curvature flows. This is done by determining the leading coefficient in the asymptotics of the many-vectors limit for an online version of the vector balancing problem, best known as the Komlós problem, and showing it is exactly determined by the extinction time for mean curvature flow. The proof builds upon Spencer's vector balancing games, Kohn and Serfaty's subsequent work on deterministic games and mean curvature flow, and Banaszczyk's Euclidean analogue of the Beck-Fiala theorem. As a consequence of this geometric characterization we are able to show the leading coefficient grows like the square root of the logarithm of the dimension. This is joint work with Nestor Guillen. We honor the memory of Robert Kohn, whose constant encouragement and generous sharing of ideas and feedback made this project possible.