Seminar Calendar
for events the day of Tuesday, April 10, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, April 10, 2012

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by ford.
 Andrew Shallue (Illinois Wesleyan Univ. Math)A sieve strategy for irreducible tabulationAbstract: An interesting open problem is to prove that $x^n + x^3 + 1$ is irreducible over $\mathbb{F}_2[x]$ infinitely often. While searching for a better algorithmic method for tabulating such irreducibles, Jonathan Webster and I have developed a sieving strategy which is rare in such settings. The Legendre Sieve provides an initial result on the sparseness of such polynomials with no small factors.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by franklan.
 Qayum Khan (University of Notre Dame)Rigidity of pseudo-free group actions on contractible manifoldsAbstract: Joint with Frank Connolly (U Notre Dame) and Jim Davis (Indiana U). We discuss Quinn's equivariant generalization of the Borel Conjecture. This concerns cocompact proper actions of a discrete group $\Gamma$ on a Hadamard manifold $X$. We give a complete solution when the action of $\Gamma$ is pseudo-free and when $X$ more generally is a $\mathrm{CAT}(0)$ manifold. Here, pseudo-free means that the singular set is discrete. A rich class of examples is obtained from crystallographic groups $\Gamma$ made out of isometric spherical space form groups $G$. If $\Gamma$ has no elements of order two, then we obtain equivariant topological rigidity of the pair $(X, \Gamma)$. Hence, if $\Gamma$ is torsion-free, then we generalize a recent theorem of A. Bartels and W. Lück, which validates the classical Borel Conjecture for $\mathrm{CAT}(0)$ fundamental groups. Otherwise, if $\Gamma$ has elements of order two, we show how to parameterize all possible counter-examples, in terms of Cappell's $\mathrm{UNil}$ summands of the L-theory of infinite dihedral groups. In certain cases, these are detected along hypersurfaces in the orbifold $X / \Gamma$ by generalized Arf invariants.

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by jathreya.
 Maxim Arnold (Department of Mathematics, University of Illinois at Urbana-Champaign)On the identical configurations of abelian sandpile model.Abstract: The Abelian sandpile model was introduced by Bak in the attempt to describe avalanche formations. During the next two decades it was intensively studied and many connections to the similar models was discovered. In particular the set of most often configurations of ASM can be considered as a representation of very natural abelian group. I shall shortly introduce the dynamics corresponding to ASM and state some results concerning identity of this group acting on Sierpinski graph.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Abstract approach to Ramsey theory and Ramsey theorems for finite treesAbstract: I will show how certain Ramsey results for finite trees (some old, some new) are obtained by applying an abstract approach to Ramsey theory. A streamlined version of this abstract approach will be explained in the talk.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by rsong.
 Yufeng Shi (University of Central Florida and Shandong University )Backward Stochastic Integral EquationsAbstract: In this talk we introduce a Volterra type of backward stochastic integral equations, i.e. so called backward stochastic Volterra integral equations (BSVIEs in short), which are natural generalization of backward stochastic differential equations (BSDEs in short). We will present some survey of old and introductory results, followed by some most recent developments, including M-solutions, S-solutions, C-solutions, Lp solutions, multi-dimensional comparison theorem, and mean-field BSVIEs. Main motivations of studying such kind of equations are as follows: (i) in studying optimal controls of (forward) stochastic Volterra integral equations, such kind of equations are needed when a Pontryagin type maximum principle is to be stated; (ii) in measuring dynamic risk for a position process in continuous time, such an equation seems to be suitable; (iii) when a differential utility needs to be considered with possible time-inconsistent preferences, one might want to use such equations.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 10, 2012
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Submitted by kkirkpat.
 Nevena Maric   [email] (U Missouri - St Louis)A construction of bivariate distributions with arbitrary marginals and specified correlationAbstract: We propose a simple and efficient algorithm for exact generation of bivariate samples from two arbitrary (possibly different) marginal distributions and with any attainable correlation coefficient (positive or negative). Our algorithm is related to the ideas of trivariate reduction (introduced by Arnold in 1967) in a sense that we use three independent uniforms in order to obtain a pair of correlated variables with desired marginals. This way we construct a bivariate distribution that is a mixture of Fr\'echet bounds and marginal products. The method allows for fast simulation, and does not have any theoretical limitation in terms of types of distributions and ranges of correlations. [joint work with Vanja Dukić]

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by darayon2.
 Peter McNamara (Stanford)Finite dimensional representations of KLR algebras Abstract: Khovanov-Lauda-Rouqier algebras are a family of algebras that appear in categorifying quantum groups. I will talk about the category of finite-dimensional representations of these algebras - classifying the simple representations, giving some understanding of higher Ext groups, and the related combinatorial structures. No previous knowledge of KLR algebras will be assumed.

Algebraic Geometry
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by nevins.
 Sarah Kitchen (Albert-Ludwigs-Universität Freiburg)Koszul categories and mixed Hodge modulesAbstract: In this talk, I will report on joint work with Pramod Achar. We considered the following problem: Can we generate a Koszul category from the category of mixed Hodge modules on a smooth complex variety X (constructible along an affine stratification S) by a general procedure, which gives a grading on the category of S-constructible rational perverse sheaves on X? We were motivated by the fact that in their paper on Koszul Duality, Beilinson, Ginzburg and Soergel (BGS) produce their grading from mixed Hodge modules in a way specific to the Bruhat stratification of a flag variety, whereas their approach to l-adic perverse sheaves was more general. I will explain how to "winnow" the category of mixed Hodge modules to come up with the desired Koszul category, and how to obtain a grading on S-constructible perverse sheaves from this, plus the relationship to the grading obtained by BGS.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 10, 2012
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Submitted by west.
 Robert E. Jamison (UIUC and Clemson University)Convexity Partition Numbers and MatchingsAbstract: In 1921 Radon showed that any $d+2$ points in ${\mathbb R}^d$ can be partitioned into two parts so that the convex hulls of the parts have nonempty intersection. In 1966 Tverberg generalized Radon's theorem to partitions into $m$ parts. These notions carry over naturally to any abstract space with a notion of convex hull. For such a space, the $m$-th partition number is the smallest integer $p_m$ such that any $p_m$ points can be partitioned into $m$ parts with the convex hulls of the parts having nonempty intersection. Radon's theorem for $m=2$ and Tverberg's theorem in general yield $p_m = (m-1)(d+1)+1$ for ordinary convexity on ${\mathbb R}^d$. Calder conjectured that Euclidean convexity is the extremal case: $p_m \le (m-1)(p_2-1)+1$ for any abstract convexity space. Eckhoff popularized this, now known as the Partition Conjecture. In 1981 Jamison used matchings in graphs to prove the Partition Conjecture for a class of convexities including partially ordered sets, trees, certain semilattices, and related structures. The purpose of this talk is to solicit improvements of Jamison's matching results that yield additional bounds on partition numbers.