Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Tue, 14 Oct 2025

14:00 - 15:00
L4

An exponential upper bound on induced Ramsey numbers

Marcelo Campos
(Instituto Nacional de Matemática Pura e Aplicada (IMPA))
Abstract
The induced Ramsey number $R_{ind}(H)$ of a graph $H$ is the minimum number $N$ such that there exists a graph with $N$ vertices for which all red/blue colorings of its edges contain a monochromatic induced copy of $H$. In this talk I'll show there exists an absolute constant $C > 0$ such that, for every graph $H$ on $k$ vertices, these numbers satisfy $R_{ind}(H) ≤ 2^{Ck}$. This resolves a conjecture of Erdős from 1975.
 
This is joint work with Lucas Aragão, Gabriel Dahia, Rafael Filipe and João Marciano.
Tue, 21 Oct 2025

14:00 - 15:00
L4

TBA

Omer Angel
(University of British Columbia)
Tue, 18 Nov 2025

15:30 - 16:30
Online

Separation of roots of random polynomials

Marcus Michelen
(Northwestern University)
Further Information

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

What do the roots of random polynomials look like? Classical works of Erdős-Turán and others show that most roots are near the unit circle and they are approximately rotationally equidistributed. We will begin with an understanding of why this happens and see how ideas from extremal combinatorics can mix with analytic and probabilistic arguments to show this. Another main feature of random polynomials is that their roots tend to "repel" each other. We will see various quantitative statements that make this rigorous. In particular, we will study the smallest separation $m_n$ between pairs of roots and show that typically $m_n$ is on the order of $n^{-5/4}$. We will see why this reflects repulsion between roots and discuss where this repulsion comes from. This is based on joint work with Oren Yakir.