Seminar Calendar
for events the day of Thursday, April 7, 2011.

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Thursday, April 7, 2011

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 7, 2011
 Del Edit Copy
Submitted by kapovich.
 Ingrid Irmer (Bonn)Distances in the homology curve complexAbstract: In this talk a curve complex HC(S) closely related to the “Cyclic Cycle Complex” (Bestvina-Bux-Margalit) and the “Complex of Cycles” (Hatcher) is deﬁned for an orientable surface of genus g ≥ 2. The main result is a simple algorithm for calculating distances and constructing quasi-geodesics in HC(S). Distances between two vertices in HC(S) are related to the “Seifert genus” of the corresponding link in S × R, and behave quite diﬀerently from distances in other curve complexes with regards to subsurface projections.

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Thursday, April 7, 2011
 Del Edit Copy
Submitted by pppollac.
 Dubi Kelmer (U Chicago Math)Logarithm laws for one parameter unipotent flowsAbstract: We establish logarithm laws for unipotent flows on certain homogeneous spaces. The main example I will discuss is the homogeneous space $X=SL(2,C)/\Gamma$. This is based on joint work with Amir Mohammadi.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, April 7, 2011
 Del Edit Copy
Submitted by aimo.
 Magdalena Musat (University of Copenhagen)Factorizable completely positive maps and the Connes embedding problemAbstract: In recent work with Uffe Haagerup, we study factorization and dilation properties of Markov maps between von Neumann algebras, motivated by the question of existence of non-factorizable Markov maps, as formulated by C. Anantharaman-Delaroche. We provide simple examples of non-factorizable Markov maps on M_n(C) for all n at least 3, as well as an example of a one-parameter semigroup (T(t)) for t\geq 0, of Markov maps on M_4(C) such that T(t) fails to be factorizable for all small values of t > 0. The existence of non-factorizable Markov maps turned out to have an interesting application to an open problem in quantum information theory, known as the asymptotic quantum Birkhoff conjecture (AQBP). We solve the conjecture in the negative by showing that every non-factorizable Markov map on M_n(C) for all n at least 3, provides a counterexample. We also discuss very recent developments concerning the question whether every factorizable map does satisfy the AQBP, and establish connections to the Connes embedding problem.

 Jonah Sinick (Department of Mathematics, University of Illinois)Real Places and Surface BundlesAbstract: Our results complement D. Calegari's result that there are no hyperbolic once-punctured torus bundles over $S^1$ with trace field having real place. We exhibit several infinite families of pairs $(-\chi, p)$ such that there exist hyperbolic surface bundles with over $S^1$ with fiber having $p$ punctures and Euler characteristic $\chi$ with trace field of having a real place. This supports our conjecture that there exist such examples for each pair $(-\chi, p)$ with finitely many known exceptions.