Combinatorial Theory Seminar

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
Tomorrow
14:00
Igor Kortchemski

Further Information: 

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

Abstract

We will be interested in the structure of random typical minimal factorizations of the n-cycle into transpositions, which are factorizations of $(1,\ldots,n)$ as a product of $n-1$ transpositions. We shall establish a phase transition when a certain amount of transpositions have been read one after the other. One of the main tools is a limit theorem for two-type Bienaymé-Galton-Watson trees conditioned on having given numbers of vertices of both types, which is of independent interest. This is joint work with Valentin Féray.

  • Combinatorial Theory Seminar
Tomorrow
15:30
Luke Postle

Further Information: 

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

Abstract

In 1943, Hadwiger conjectured that every graph with no Kt minor is $(t-1)$-colorable for every $t\geq 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$ minor has average degree $O(t(\log t)^{1/2})$ and hence is $O(t(\log t)^{1/2)}$-colorable. Recently, Norin, Song and I showed that every graph with no $K_t$ minor is $O(t(\log t)^\beta)$-colorable for every $\beta > 1/4$, making the first improvement on the order of magnitude of the $O(t(\log t)^{1/2})$ bound. Here we show that every graph with no $K_t$ minor is $O(t (\log t)^\beta)$-colorable for every $\beta > 0$; more specifically, they are $O(t (\log \log t)^6)$-colorable.

  • Combinatorial Theory Seminar
3 November 2020
15:30
TBA
Shoham Letzter

Further Information: 

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

  • Combinatorial Theory Seminar
24 November 2020
15:30
TBA
TBA

Further Information: 

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

  • Combinatorial Theory Seminar
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