Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 10, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, March 10, 2020

11:00 am in 243 Altgeld Hall,Tuesday, March 10, 2020

#### $C_2$-equivariant homotopy groups of spheres

###### Mark Behrens (Notre Dame Math)

Abstract: I will explain how $RO(C_2)$-graded $C_2$-equivariant homotopy groups of spheres can be deduced from non-equivariant stable homotopy groups of stunted projective spaces, and the computation of Mahowald invariants.

2:00 pm in 243 Altgeld Hall,Tuesday, March 10, 2020

#### Online DP-coloring of graphs

###### Sasha Kostochka (University of Illinois, Urbana-Champaign)

Abstract: It is known that the DP-chromatic number (also called correspondence chromatic number), $\chi_{DP}(G)$, and the online chromatic number (also called paintability), $\chi_{P}(G)$, of a graph $G$ are both at least the list chromatic number (also called choosability), $\chi_{\ell}(G)$, and can be significantly larger. The goal of the talk is twofold. First, we present examples of graphs $G$ with $\chi_P(G)>\chi_{DP}(G)$ (but only by $1$). Second, we introduce online DP-coloring of graphs and the online DP-chromatic number, $\chi_{DPP}(G)$. This parameter is an upper bound for both, $\chi_{P}(G)$ and $\chi_{DP}(G)$, but still has good properties of colorings: $\chi_{DPP}(G)$ is at most the degeneracy of $G$ plus $1$, a version of Brooks' Theorem holds for it, and every planar graph is online DP-colorable with $5$ colors.

This is joint work with S.-J. Kim, X. Li and X. Zhu.

3:00 pm in 243 Altgeld Hall,Tuesday, March 10, 2020

#### The critical filtration of Hurwitz spaces

###### George Shabat (Russian State University for the Humanities and Independent University of Moscow)

Abstract: Hurwitz spaces, introduced at the end of 19th century, consist of classes of isomorphism of pairs (algebraic curve, rational function on it), where a curve has a fixed genus and a function has a fixed degree. The strata of the filtration, to which the talk is devoted, are formed by the pairs, in which a function has a fixed number of \textit{critical values}. In every Hurwitz space the largest stratum (the \textit{Morse} one) is Zariski-open, while the lowest one consists of pairs in which the function has only three critical values, i.e. of \textit{Belyi pairs}. The considerable part of the talk will be devoted to the strata closest to the lowest ones, i.e. the so-called \textit{Fried families}. The combinatorial, algebro-geometric and arithmetic structures, related to these objects, will be considered, and some examples will be presented.