Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, September 30, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2014           September 2014          October 2014
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1  2       1  2  3  4  5  6             1  2  3  4
3  4  5  6  7  8  9    7  8  9 10 11 12 13    5  6  7  8  9 10 11
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Tuesday, September 30, 2014

9:00 am in Illini Rooms A & B, Illini Union,Tuesday, September 30, 2014

#### Corporate Forum

Abstract: The Corporate Forum will be held from 9 a.m. to 4 p.m. The Career Fair will run throughout the day with company presentations given concurrently. More information at http://www.math.illinois.edu/UndergraduateProgram/math-career-fair.html

11:00 am in 243 Altgeld Hall,Tuesday, September 30, 2014

#### Coassembly in algebraic K-theory

###### Cary Malkiewich   [email] (UIUC)

Abstract: The coassembly map allows us to approximate any contravariant homotopy-invariant functor by an excisive functor, i.e. one that behaves like a cohomology theory. We apply this construction to a contravariant form of Waldhausen's algebraic K-theory of spaces, and its corresponding THH functor. The results are somewhat surprising: a certain dual form of the A-theory Novikov conjecture is false, but when the space in question is the classifying space BG of a finite p-group, coassembly on THH is split surjective after p-completion. The method of proof suggests new conjectures about both the assembly and coassembly maps for the A-theory of BG. If there is time, we will also discuss related work on the equivariant structure of THH.

1:00 pm in 243 Altgeld Hall,Tuesday, September 30, 2014

#### Hitting time statistics for observations and application to random dynamical systems

###### Jerome Rousseau (Universidade Federal da Bahia/Illinois)

Abstract: We study the distribution of hitting and return times for observations of dynamical systems. We apply this results to get an exponential law for the distribution of hitting and return time for rapidly mixing random dynamical systems. For random subshifts of finite type, we analyze the distribution of hitting times with respect to the sample measures and prove that under fast mixing assumptions one can get an exponential law. View lecture at http://youtu.be/tN0jpVRCkfU

1:00 pm in 345 Altgeld Hall,Tuesday, September 30, 2014

#### Tameness in Abstract Elementary Classes

###### Will Boney (UIC)

Abstract: Tameness is a locality property of Galois types in AECs. Since its isolation by Grossberg and VanDieren 10 years ago, it has been used to prove new results (upward categoricity transfer, stability transfer) and replace set-theoretic hypotheses (existence of independence notions). In this talk, we will outline the basic definitions, summarize some key results, and discuss some open questions related to tameness.

2:00 pm in Altgeld Hall 347,Tuesday, September 30, 2014

#### A distributional equality for suprema of spectrally positive Levy processes

###### Zoran Vondracek (UIUC Math and University of Zagreb)

Abstract: Let Y be a spectrally positive Levy process with strictly negative expectation, C an independent subordinator with finite expectation, and X=Y+C. A curious distributional equality proved some ten years ago states that if the expectation of X is strictly negative, then the overall supremum of Y and the supremum of X just before the first time its new supremum is reached by a jump of C have the same distribution. In this talk I will give an alternative proof of an extension of this result and offer an explanation why it is true.

3:00 pm in 241 Altgeld Hall,Tuesday, September 30, 2014

#### On the strong chromatic index of graphs

###### Michael Santana   [email] (UIUC Math)

Abstract: A strong edge-coloring of a graph $G$ is a proper edge-coloring with the additional property that each color class forms an induced matching in $G$. The strong chromatic index of $G$ is the minimum $k$ for which $G$ has a strong edge-coloring using $k$ colors. Erdős and Nešetřil conjectured that every graph with maximum degree $\Delta$ has strong chromatic index at most $\frac{5}{4}\Delta^2$ if $\Delta$ is even, and at most $\frac{5}{4}\Delta^2 - \frac{1}{2}\Delta + \frac{1}{4}$ if $\Delta$ is odd. If true, both cases are best possible. In 1990, Faudree, Gyárfás, Schelp, and Tuza revised this conjecture of Erdős and Nešetřil for planar graphs with maximum degree at most 3, stating that such graphs should have strong chromatic index at most 9. We verify this conjecture, which is best possible, and extend it to loopless multigraphs. In addition to our result, I will present several unresolved conjectures and areas for further research. This is joint work with A.V. Kostochka, X. Li, W. Ruksasakchai, T. Wang, and G. Yu.

3:00 pm in 243 Altgeld Hall,Tuesday, September 30, 2014