Seminar Calendar
for events the day of Tuesday, February 28, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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1  2  3  4  5  6  7             1  2  3  4                1  2  3
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Tuesday, February 28, 2012

Ergodic Theory
11:00 am   in 347 Altgeld Hall,  Tuesday, February 28, 2012
 Del Edit Copy
Submitted by jathreya.
 Francois Ledrappier (Notre Dame)Entropy rigidity for non-positively curved compact manifolds.Abstract: We consider different asymptotic rates related to the geometry of the universal cover of a compact manifold. We discuss relations between these rates, a characterization of symmetric spaces of non-positive curvature and related problems.

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by franklan.
 Paul Goerss (Northwestern University)Brown-Comenetz duality in the K(2)-local categoryAbstract: The principal result I will discuss is the identification of the homotopy type of the Brown-Comenetz dual of the K(2)-local sphere at p=3. Given the rather technical nature of this computation, I will probably spend more time on why this is an interesting question than on techniques of proof.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by berdogan.
 Andrew Lawrie (U Chicago Math)Scattering for wave maps exterior to a ballAbstract: In this talk I will discuss some recent work that was completed in collaboration with Professor Wilhelm Schlag. We consider $1$-equivariant wave maps from $\mathbb{R}_t\times (\mathbb{R}^3_x\setminus B) \to S^3$ where $B$ is a ball centered at $0$, and $\partial B$ gets mapped to a fixed point on~$S^3$. We show that $1$-equivariant maps of degree zero scatter to zero irrespective of their energy. For positive degrees, we prove asymptotic stability of the unique harmonic maps in the energy class determined by the degree.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by ssolecki.
 Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)Point realizations of Boolean actionsAbstract: I will show that if $M$ is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from $M$ to $U(1)$ on a separable probability algebra which preserves the measure and yet does not admit a point realization in the sense of Mackey. This is in contrast with Mackey's point realization theorem for locally compact, second countable groups. The proof of the above theorem goes through showing certain results concerning the infinite dimensional Gaussian measure space $({\mathbb C}^{\mathbb N},\gamma_\infty)$ which contrasts the Cameron--Martin Theorem. I will place the main result in the background of recent work on point realization and lack thereof for various classes of Polish groups. These results are due to Becker, Glasner, Tsirelson, Weiss, Kwiatkowska and myself. This is a joint work with Justin Moore.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by kkirkpat.
 Scott Armstrong   [email] (U Wisconsin Math)Random homogenization of Hamilton-Jacobi equationsAbstract: I will describe some recent work with Souganidis on the stochastic homogenization of Hamilton-Jacobi equations (both "viscous" as well as first-order equations). The homogenization of special cases of these equations has a direct connection to the work of Sznitman on the quenched large deviations of Brownian motion in the presence of Poissonian obstacles. It also benefits from some strong analogies to certain aspects of the theory of first-passage percolation.

Graph Theory and Combinatorics
3:00 pm   in Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by west.
 Alexandr Kostochka (Department of Mathematics, University of Illinois at Urbana-Champaign)Ks,t-minors in dense graphs and in (s+t)-chromatic graphsAbstract: We refine two known results on the existence of $K_{s,t}$-minors in graphs. First we prove that if $(t/\log_2 t)\ge 1000s$, then every graph $G$ with average degree at least $t+8s\log_2 s$ has a $K^*_{s,t}$-minor, where $K^*_{s,t}$ is the graph obtained from $K_{s,t}$ by adding the edges of a complete graph on the first partite set. This result refines a result by Kühn and Osthus and is joint work with N. Prince. It was proved earlier that for sufficiently large $t$ in terms of $s$, every graph with chromatic number $s+t$ has a $K^*_{s,t}$-minor. In particular, with $t_0(s) = \max\{4^{15s^2+s},(240s\log_2{s})^{8s\log_2{s}+1}\}$, the conclusion holds when $t>t_0(s)$. This result confirmed a special case of a conjecture by Woodall and Seymour. We show that the conclusion holds already for much smaller $t$, namely, for $t>C(s\log s)^3$.

Mathematics Colloquium - Special Lecture 2011-12
4:00 pm   in 245 Altgeld Hall,  Tuesday, February 28, 2012
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Submitted by kapovich.
 Rui Loja Fernandes (Instituto Superior Tecnico, Portugal)Stability of LeavesAbstract: I will start by recalling some classical results on stability of periodic orbits of flows (Poincaré), of leaves of foliations (Reeb-Thurston), and of orbits of group actions (Hirsch-Stowe). Then I will explain a new result on stability of symplectic leaves in Poisson geometry (joint work with M. Crainic) and how all these apparent distinct results can be related using Lie groupoid theory. Time permitting, I will state a related conjecture in KAM theory.