Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 16, 2021.

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Tuesday, February 16, 2021

11:00 am in Zoom,Tuesday, February 16, 2021

Understanding accessible infinity-categories

Charles Rezk   [email] (UICU)

Abstract: Lurie introduced the very important notion of "accessible infinity-category", a generalization of the more classical notion of "accessible category". These are (infinity-)categories which are produced from two pieces of data: a small (infinity-)category and a "regular cardinal". The goal of this talk is to give an introduction to some of the ideas surrounding these, and to put them in a broader context.

Email vesna@illinois.edu for zoom info.

11:00 am in Zoom,Tuesday, February 16, 2021

Landau-Siegel zeros and central values of L-functions

Kyle Pratt (Oxford)

Abstract: Researchers have tried for many years to eliminate the possibility of Landau-Siegel zeros---certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of $L$-functions at the central point.

2:00 pm in Zoom,Tuesday, February 16, 2021

A proof of the Erdős–Faber–Lovász conjecture

Abhishek Methuku (University of Birmingham)

Abstract: The celebrated Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this talk, I will sketch a proof of this conjecture for every large n.

Joint work with D. Kang, T. Kelly, D. Kühn and D. Osthus.

For Zoom information, please contact Sean at SEnglish (at) illinois (dot) edu.