Department of

Mathematics


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

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2020            March 2020             April 2020     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                    1    1  2  3  4  5  6  7             1  2  3  4
  2  3  4  5  6  7  8    8  9 10 11 12 13 14    5  6  7  8  9 10 11
  9 10 11 12 13 14 15   15 16 17 18 19 20 21   12 13 14 15 16 17 18
 16 17 18 19 20 21 22   22 23 24 25 26 27 28   19 20 21 22 23 24 25
 23 24 25 26 27 28 29   29 30 31               26 27 28 29 30      
                                                                   

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.