Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, November 17, 2020.

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Tuesday, November 17, 2020

11:00 am in Zoom,Tuesday, November 17, 2020

Vector bundles on projective spaces

Morgan Opie (Harvard Univfersity)

Abstract: Given the ubiquity of vector bundles, it is perhaps surprising that there are so many open questions about them -- even on projective spaces. In this talk, I will outline some results about vector bundles on projective spaces, including my ongoing work on complex rank 3 topological vector bundles on CP^5. In particular, I will describe a classification of such bundles which involves a surprising connection to topological modular forms; a concrete, rank-preserving additive structure which allows for the construction of new rank 3 bundles on CP^5 from simple ones; and future directions related to this project.

Please email vesna@illinois.edu for Zoom info.

2:00 pm in Zoom,Tuesday, November 17, 2020

Further progress towards Hadwiger's conjecture

Luke Postle (University of Waterloo)

Abstract: Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t\ge 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$ minor has average degree $O(t\sqrt{\log t})$ and hence is $O(t\sqrt{\log t})$-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 $O(t\sqrt{\log t})$ 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.

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