Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 30, 2018.

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Tuesday, January 30, 2018

11:00 am in 345 Altgeld Hall,Tuesday, January 30, 2018

Localizing the E_2 page of the Adams spectral sequence

Eva Belmont (MIT)

Abstract: The Adams spectral sequence is one of the central tools for calculating the stable homotopy groups of spheres, one of the motivating problems in stable homotopy theory. In this talk, I will discuss an approach for computing the Adams E_2 page at p = 3 in an infinite region, by computing its localization by the non-nilpotent element b_{10}. This approach relies on computing an analogue of the Adams spectral sequence in Palmieri's stable category of comodules, which can be regarded as an algebraic analogue of stable homotopy theory. This computation fits in the framework of chromatic homotopy theory in the stable category of comodules.

12:00 pm in 243 Altgeld Hall,Tuesday, January 30, 2018

To Be Announced

Ilya Kapovich   [email] (Illinois Math)

3:00 pm in 241 Altgeld Hall,Tuesday, January 30, 2018

An improved upper bound for the (5,5)-coloring number of K_n

Emily Heath (Illinois Math)

Abstract: A $(p,q)$-coloring of a graph $G$ is an edge-coloring of $G$ in which each $p$-clique contains edges of at least $q$ distinct colors. We denote the minimum number of colors needed for a $(p,q)$-coloring of the complete graph $K_n$ by $f(n,p,q)$. In this talk, we will describe an explicit $(5,5)$-coloring of $K_n$ which proves that $f(n,5,5)\leq n^{1/3+o(1)}$ as $n\rightarrow\infty$, improving the best known probabilistic upper bound of $O(n^{1/2})$ given by Erdős and Gyrfs. This is joint work with Alex Cameron.