Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 1, 2013.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2013          October 2013          November 2013
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1  2  3  4  5  6  7          1  2  3  4  5                   1  2
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Tuesday, October 1, 2013

11:00 am in 243 Altgeld Hall,Tuesday, October 1, 2013

#### Goodwillie's classification of homogeneous functors

###### Randy McCarthy (UIUC)

Abstract: We will discuss Goodwillie's classification of homogeneous functors of model categories. Our focus will be primarily on how one passes from the based to the unbased setting after first introducing the basic theory and recalling the more familiar classification in the based setting.

1:00 pm in 345 Altgeld Hall,Tuesday, October 1, 2013

#### Quantum Computing: A Field Report

###### Yuri Gurevich (Quantum Architecture and Computing, Microsoft Research)

Abstract: This talk is primarily for quantum-naive mathematicians wishing to hear from one of their own who wondered (first, quite a while ago, to computer science and recently) to the quantum land. I'll attempt to describe what quantum computing is. Quantum experts may be bored (though, if they survive to the end, they'll hear a quick update on the D-Wave machine, the first commercial quantum computer).

2:00 pm in 345 Altgeld Hall,Tuesday, October 1, 2013

#### Reflection factorizations of Singer cycles

###### Joel Lewis (U. Minnesota)

Abstract: A classical combinatorial result (originally due to Denes) is that there are precisely n^(n - 2) factorizations of a long cycle in the symmetric group S_n as a product of n - 1 transpositions.  This result has subsequently been generalized in many directions, e.g., to factorizations of Coxeter elements in a (real or complex) reflection group.  In this talk, I'll discuss joint work with Vic Reiner and Dennis Stanton on a q-analogue, replacing the symmetric group with the general linear group GL_n(F_q), the long cycle with a Singer cycle, and transpositions with reflections.  Using the (ordinary) representation theory of GL_n, we've shown that the number of shortest such factorizations is (q^n - 1)^(n - 1).  I'll discuss this result, as well as some extensions and open questions.

2:00 pm in Altgeld Hall 347,Tuesday, October 1, 2013

#### Central Limit Theorems for Supercritical Branching Markov Processes

###### Rui Zhang (UIUC Math)

Abstract: In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems proved in Adamczak and Milos (2011) for branching OU processes with binary branching mechanisms. Compared with the results of Adamczak and Milos (2011), our central limit theorems are more satisfactory in the sense that the normal random variables in our theorems are non-degenerate. This is a joint work with Yan-Xia Ren and Renming Song.

3:00 pm in 241 Altgeld Hall,Tuesday, October 1, 2013

#### Compactness and finitely forcible graphons

###### Jan Volec   [email] (University of Warwick)

Abstract: Graphons are limit objects that are associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons determined by finitely many subgraph densities, which are referred to as finitely forcible graphons. In 2011, Lovasz and Szegedy asked several questions about the complexity of the topological space of so-called typical vertices of a finitely forcible graphon. In particular, they conjectured that the space is always compact. We disprove the conjecture by constructing a finitely forcible graphon such that the associated space of typical vertices is not compact. In fact, our construction actually provides an example of a finitely forcible graphon with the space which is even not locally compact. This is a joint work with Roman Glebov and Dan Kral.

3:00 pm in 347 Altgeld Hall,Tuesday, October 1, 2013

#### Anticorrelated Sampling Techniques for Variance-reduced Simulation of Markov Processes

###### Matthew West (UIUC MechSE)

Abstract: Accurate stochastic simulation benefits from reduction of sampling variance and, consequently, computational cost. We extend classical variance reduction techniques (antithetic and stratified sampling) for application to continuous-time Markov jump processes. Our algorithms introduce localized anticorrelation between samples to reduce variance in mean estimates, and apply to both exact SSA and approximate tau-leaping simulation methods. Significant reductions in computational cost are achievable for linear and nonlinear systems, as demonstrated by analytical results and numerical examples.

4:00 pm in 243 Altgeld Hall,Tuesday, October 1, 2013

#### Introduction to Grothendieck Topologies

###### Juan S. Villeta-Garcia (UIUC Math)

Abstract: We will introduce Grothendieck topologies, sites, sheaves on them, and their cohomology. Examples will be taken from scheme theory and commutative algebras. The exposition will be basic and aimed at beginners (such as the speaker). This will be the first of a two-part talk. Professors are welcome to attend.