Department of

Mathematics

Seminar Calendar
for events the day of Tuesday, April 26, 2016.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, April 26, 2016

11:00 am in 345 Altgeld Hall,Tuesday, April 26, 2016

Motivic vector bundles on CP^n

Aravind Asok (USC)

Abstract: It is a classical problem to determine which complex topological vector bundles on CP^n admit an algebraic structure. We will discuss obstructions" to equipping a bundle with an algebraic structure coming from A^1-homotopy theory (though I won't presuppose any knowledge of A^1-homotopy theory). The main goal of the talk is to analyze the question of whether some rank 2 bundles on CP^n constructed by Elmer Rees using homotopy theoretic techniques admit an algebraic structure. This talk is based on joint work with Jean Fasel and Mike Hopkins.

12:00 pm in Altgeld Hall 243,Tuesday, April 26, 2016

The geometry of hyperbolic free group extensions

Spencer Dowdall (Vanderbilt University)

Abstract: Each subgroup $\Gamma$ of the outer automorphism group of a free group naturally gives rise to a group extension $E_\Gamma$ of the free group. In joint work with Sam Taylor, we have given geometric conditions on $\Gamma$ that imply the extension is a hyperbolic group. After describing these conditions, I will present recent results about the fine geometric structure of these group extensions. These results include a Scott--Swarup type theorem proving quasiconvexity of infinite-index subgroups of the free group and a width theorem that characterizes these hyperbolic extensions in terms of the axes of primitive elements of the free group.

1:00 pm in 243 Altgeld Hall,Tuesday, April 26, 2016

Long term dynamics of nonlinear wave equations

Wilhelm Schlag (U Chicago Math)

Abstract: We will describe some of the progress achieved over the past few years on the asymptotic description of solutions to semilinear wave equations. The results draw on both analytical methods such as concentration compactness and ideas from dynamical systems (invariant manifolds, foliations). The latter is especially helpful in the presence of dissipation.

1:00 pm in 345 Altgeld Hall,Tuesday, April 26, 2016

Tame Topology over dp-minimal structures

Erik Walsberg (Paris VI)

Abstract: We discuss topological properties of definable sets and functions in dp-minimal expansions of ordered abelian groups and valued fields. Some properties of definable sets and functions in o-minimal expansions of ordered abelian groups extend to this setting.

2:00 pm in 347 Altgeld Hall,Tuesday, April 26, 2016

Tail process and its role in limit theorems

Bojan Basrak (University of Zagreb)

Abstract: We discuss how tail process captures dependence structure of a stationary regularly varying sequence. This theory is applied to extend various limiting results from iid setting to dependent sequences, as long as their dependence declines in time. We will also discuss the convergence of partial sums and other functionals of regularly varying sequences, covering some recent and not yet published results.

3:00 pm in 241 Altgeld Hall,Tuesday, April 26, 2016

Incidence coloring of graphs and oriented incidence coloring of digraphs

Andre Raspaud (Bordeaux University)

Abstract: Brualdi and Massey defined incidence coloring while studying the strong edge chromatic index of bipartite graphs. An incidence of an undirected graph G is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge of $G$ incident with $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent if one of the following holds: (i) $v = w$, (ii) $e = f$ or (iii) $vw = e$ or $f$. An incidence coloring of $G$ assigns a color to each incidence of $G$ in such a way that adjacent incidences get distinct colors. In this talk we present bounds for incidence chromatic number of graphs having high maximum average degree. In particular we prove that every graph with maximum degree at least $7$ and with maximum average degree strictly less than $4$ admits a $(\Delta+3)$-incidence coloring. This result implies that every triangle free planar graph with maximum degree at least $7$ is $(\Delta+3)$-incidence colorable. We will also introduce a similar concept for digraphs and define the oriented incidence chromatic number. Using digraph homomorphism, we show that the oriented incidence chromatic number of a digraph is closely related to the chromatic number of the underlying simple graph. This motivates our study of the oriented incidence chromatic number of symmetric complete digraphs. We give upper and lower bounds for the oriented incidence chromatic number of these graphs, as well as digraphs arising from common graph constructions and decompositions.

4:00 pm in 245 Altgeld Hall,Tuesday, April 26, 2016