YouTube channel

Schedule of talks:

Abstracts

(A. Yavicoli): Let E be a measurable set of positive Lebesgue measure on the real line. A simple argument using a density point shows that E contains a translated and rescaled copy of every finite subset of the real line. What happens if we replace a finite set by an infinite one? Erdös conjectured that the answer changes completely: for every infinite set A, there should be a measurable set E of positive measure that contains no translated and rescaled copy of A. I will introduce this conjecture, explain some of the ideas surrounding it, and discuss recent progress toward its resolution.

(S. Fenley): Anosov flows are flows that admit invariant stable and unstable bundles, which are respectively contracted or expanded when flowing forward. The Verjosky conjecture states that every codimension one Anosov flow in dimensions 4 or higher is orbitally equivalent to a suspension Anosov flow. Codimension one means that either the weak stable or the weak unstable foliation of the flow has codimension one. This conjecture is 50 years old. In joint work with K. Mann and R. Potrie, we construct infinitely many counterexamples to the conjecture in 4-manifolds. To achieve that, we need a closed hyperbolic 3-manifold M, a faithful minimal representation of \pi_1(M) into Homeo+(S^1) (the circle), and a group equivariant Cannon-Thurston map f from S^1 to the sphere at infinity of hyperbolic 3-space. With this data we can construct a topological Anosov flow in dimension 4. If the set of non injective points of the map f has image in the sphere at infinity which has measure zero, we show how to perturb the topological Anosov flow to obtain a (smooth) Anosov flow, which is orbitally equivalent to it. We then show that there are infinitely many examples satisfying the data, producing counterexamples to the Verjovsky conjecture.

(Y. Yuan):

(A. Barvinok):

(A. Gelb):

(P. Hajlasz):

Past Ohio State University Mathematics Department Colloquia

• 2025-2026

• 2024-2025

• 2023-2024

• 2022-2023

• 2020-2021

• 2019-2020

• 2018-2019

• 2017-2018

• 2016-2017

(V. Kobzar): We establish a direct connection between combinatorial discrepancy minimization problems and curvature flows in R^m. This is done by determining the long-time asymptotics of an online version of the classic vector balancing problem, known as the Komlós conjecture, and showing it is exactly determined by the extinction time of mean curvature flow on the m-dimensional cube. Our proof builds upon Kohn and Serfaty's 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 show that the leading order term of the value of this game grows as \Theta (\sqrt { T \log m}) as the time horizon T gets large. This is joint work with Nestor Guillen at Courant available here. A geometric PDE-inspired perspective is also fruitful in the more classic, offline Komlós setting, and I will briefly preview our most recent results in this direction at the end of the talk.

This page is maintained by Marjorie Drake.