UIUC Dept. of Mathematics Seminar Calendar

     January 2012          February 2012            March 2012     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
  1  2  3  4  5  6  7             1  2  3  4                1  2  3
  8  9 10 11 12 13 14    5  6  7  8  9 10 11    4  5  6  7  8  9 10
 15 16 17 18 19 20 21   12 13 14 15 16 17 18   11 12 13 14 15 16 17
 22 23 24 25 26 27 28   19 20 21 22 23 24 25   18 19 20 21 22 23 24
 29 30 31               26 27 28 29            25 26 27 28 29 30 31

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.

Harmonic Analysis and Differential Equations
1:00 pm in 347 Altgeld Hall, Tuesday, February 28, 2012

Del

Edit

Copy

Submitted by berdogan.

Andrew Lawrie (U Chicago Math)
Scattering for wave maps exterior to a ball
Abstract: 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

Del

Edit

Copy

Submitted by ssolecki.

Slawomir Solecki (Department of Mathematics, University of Illinois at Urbana-Champaign)
Point realizations of Boolean actions
Abstract: 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.

Graph Theory and Combinatorics
3:00 pm in Altgeld Hall, Tuesday, February 28, 2012

Del

Edit

Copy

Submitted by west.

Alexandr Kostochka (Department of Mathematics, University of Illinois at Urbana-Champaign)
K_s,t-minors in dense graphs and in (s+t)-chromatic graphs
Abstract: 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 $t>C(s\log s)^3$.