Seminar Calendar
for events the day of Tuesday, April 3, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, April 3, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by jathreya.
 Joshua Bowman (Stony Brook)Basins of infinity for polynomial maps of $\mathbb{C}^2$Abstract: Basins of attraction in holomorphic dynamics are well understood in dimension 1, much less so in higher dimensions. We will consider regular polynomial maps of $\mathbb{C}^2$ (maps which extend to endomorphisms of $\mathbb{P}^2$) and describe some tools for studying their basins of infinity. We show that there exist endomorphisms of $\mathbb{P}^2$ whose basins of infinity have infinitely generated second homology.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by ford.
 Benjamin Smith (INRIA Saclay and Ecole Polytechnique Paris)Point counting on genus 2 curves with real multplicationAbstract: Point counting -- that is, computing zeta functions of curves over finite fields --- is a fundamental problem in algorithmic number theory and cryptography. In this talk, we present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Using our new algorithm, we can compute the zeta function of an explicit RM genus 2 curve over $\mathbb{F}_q$ in $O(\log^5 q)$ bit operations (vs. $O(\log^8 q)$ for the classical algorithm). This, together with a number of other practical improvements, yields a dramatic speedup for cryptographic-sized Jacobians over prime fields, as well as some record-breaking computations. (Joint work with D. Kohel and P. Gaudry)

Topology Seminar
11:00 am   Tuesday, April 3, 2012
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Submitted by franklan.
 No seminar todayAbstract: We resume next week.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by phierony.
 Robert E. Jamison (Clemson/UIUC)A Dependency Calculus for Finitary ClosuresAbstract: A closure system consists of a ground set $X$ together with a family $\mathscr{C}$ of closed subsets of $X$. The only requirements are that $\mathscr{C}$ is closed under arbitrary intersections and contains $X$. Thus each subset $S$ of $X$ lies in a smallest closed set $\mathscr{C}(S)$. The map $S \to \mathscr{C}(S)$ is the closure operator. The closure operator is finitary provided whenever $p \in \mathscr{C}(S)$, there is a finite subset $E$ of $S$ with $p \in \mathscr{C}(E)$. In this talk a first order logic for finitary closure operators will be presented. This first order logic can be used to describe and systematize the study of most important properties of finitary systems. In particular, I will describe a classification scheme for many of the important classes of finitary closures (matroids, antimatroids, partial order convexity, etc). Moreover, I will describe several metatheorems concerning classical convexity invariants such as the Helly and Radon numbers.

Algebra, Geometry and Combinatoric
2:00 pm   in 345 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by darayon2.
 Bridget Tenner (DePaul University)Repetitions and patternsAbstract: A permutation $w$ can be written as a product of adjacent transpositions, and such a product of shortest length, $\ell(w)$, is called a reduced decomposition of $w$. The difference between $\ell(w)$ and the number of distinct letters appearing in a (any) reduced decomposition of $w$ is $\text{rep}(w)$; that is, this statistic describes the amount of repetition in a reduced decomposition of $w$. In this talk, we will explore this statistic $\text{rep}(w)$, and find that it is always bounded above by the number of 321- and 3412-patterns in $w$. Additionally, these two quantities are equal if and only if $w$ avoids the ten patterns 4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, and 45231.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 3, 2012
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Submitted by kkirkpat.
 Jun Yin (U Wisconsin-Madison)Eigenvalue and Eigenvector distributions of Random matricesAbstract: In the current study of the random matrix theory, many long time open problems have been solved in the past three years. Right now, the study of the distribution of individual eigenvalues, even eigenvectors has become possible. In some works, we even obtained some brand new formulas which were not predicted before. And our methods have been successfully applied on many different matrix ensembles, like (generalized) Wigner matrix, covariance matrix, band matrix, Erdoes-renyi Graph, correlation matrix, etc. In this talk, besides the recent process on random matrix theory, we will also introduce the main open questions in this field.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by katz.
 Sheldon Katz   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Quantum Cohomology of Toric VarietiesAbstract: The structure of the quantum cohomology ring of a smooth projective toric variety was described by Batyrev and proven by Givental as a consequence of his work on mirror symmetry. This talk is in part expository since some details were never written down by Givental. I conclude with some open questions related to the quantum cohomology ring and the quantum product. An extension of these questions play a foundational role in the development of quantum sheaf cohomology which has been undertaken jointly with Donagi, Guffin, and Sharpe. Given a smooth projective variety X and a vector bundle E with $c_i(E)=c_i(X)$ for i=1,2, the quantum sheaf cohomology ring of string theory is supposed to be a deformation of the algebra $H^*(X,\Lambda^*E^*)$. If E=TX, quantum sheaf cohomology is the same as ordinary quantum cohomology.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by west.
 Thomas Mahoney (UIUC Math)Extending graph choosability results to paintabilityAbstract: Introduced independently by Schauz and by Zhu, the Marker-Remover game is an on-line version of list coloring. The resulting graph parameter, paintability, is at least the list chromatic number (also known as "choosability"). We strengthen several choosability results to paintability. We study paintability of joins with complete or empty graphs. We determine upper and lower bounds on the paintability of complete bipartite graphs. We characterize 3-paint-critical graphs and show that claw-free perfect graphs with $\omega(G)\le3$ have paintability equal to chromatic number. Finally, we introduce and study sum-paintability, the analogue of sum-choosability.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Tuesday, April 3, 2012
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Submitted by kapovich.
 Igor Rivin (Temple University)Conformal matching of proteinsAbstract: The question of whether two proteins can bind, and how, is one of the canonical problems in molecular biology, where it is sometimes known as the protein docking problem. This question has, so far, been studied primarily by ad hoc methods (such as Monte Carlo simulation). In this talk I will discuss some ideas and work in progress (some joint with Joel Hass of UC Davis) on using discrete (and not so discrete) conformal geometry to attack the problem, and the interesting (to the speaker, anyhow) mathematical questions which arise.