| January 15 | Erik Guentner | Approximation in group C*-algebras (part 1) | |||
| University of Hawaii at Manoa | |||||
| January 22 | No talk | (due to a job talk, see http://www.math.vanderbilt.edu/~colloq/) | |||
| January 29 | No talk | (due to a job talk, see http://www.math.vanderbilt.edu/~colloq/) | |||
| February 5 | No talk | (due to a faculty meeting) | |||
| February 12 | Erik Guentner | Approximation in group C*-algebras (part 2) | |||
| University of Hawaii at Manoa | |||||
| February 19 | No talk | ||||
| February 26 | Erik Guentner | Approximation in group C*-algebras (part 3) | |||
| University of Hawaii at Manoa | |||||
| March 4 | No talk | (Spring break) | |||
| March 11 | Yves de Cornulier | Property T for the groups SL_n(Z[x_1,...,x_d]) for all d and all n>2, after Shalom and Vaserstein. | |||
| IRMAR, Univ. of Rennes I | Abstract: Shalom recently proved that for R=Z[x_1,...,x_d] and n>2, if the "universal SL_n" SL_n(R) satisfies the following "bounded reduction": every matrix in SL_n(R) is a bounded product of elementary matrices and matrices in SL_{n-1}(R), then SL_n(R) has Property T. He also observed that the bounded reduction holds provided that n>d+2. Vaserstein subsequently proved that the bounded reduction holds for every d and n>2. I'll try to sketch the proof of these two results. (Other more informal talks are to be planned, in order to look more thoroughly into the proof, if part of the audience is interested). | ||||
| March 18 | No talk | ||||
| March 25 | Bogdan Nica | Relatively spectral morphisms and applications to K-theory | |||
| Vanderbilt University | Abstract: Spectrum-preserving morphisms between Banach algebras are useful for comparing their K-theory and their ``noncommutative dimensions'' as expressed by various notions of stable ranks. It may happen, however, that the preservation of the spectrum is only known over a dense subalgebra. This talk is concerned with such "relatively" spectral morphisms. | ||||
| April 1 | Jerry Kaminker | Higher spectral flow | |||
| IUPUI | Abstract: It is well known that the bounded self-adjoint Fredholm operators with both positive and negative essential spectrum provide a classifying space for odd K-theory. One can also consider analogous families of unbounded self-adjoint Fredholm operators. One is then led to study the eigenspaces of the operators and how they vary with the goal of obtaining invariants of the family. We will discuss some results obtained taking this point of view which relate the multiplicity of the spectrum to the triviality of the family as an element of K-theory. This is joint work with Ron Douglas. | ||||
| April 8 | Piotr Nowak | Isoperimetry of group actions | |||
| Vanderbilt University | Abstract: The notion of isoperimetric profiles is a generalization of isoperimetric dimension, which is a large-scale invariant. In the context of discrete groups isoperimetric profiles were introduced by Vershik, but were well-defined only for amenable groups. The purpose of this talk is a definition of an isoperimetric profile of an action of a finitely generated group on a compact Hausdorff space. We show that these profiles share many properties with original invariants for amenable groups/regularly exhaustible open manifolds. We also define the generalized isoperimetric profile of an amenable group via the action of G on its Stone-Cech compactification. For this last profile we explore the relation to growth and asymptotic dimension. We also compute the isoperimetric profile for several classes of groups for which the classical profile was not defined, e.g. hyperbolic groups. | ||||
| April 15 | No talk | ||||
| Shanks workshop: Special lectures by Paul Baum, dedicated to Gennadi Kasparov: | |||||
| April 21 | Paul Baum | What is K-theory and what is it good for? | |||
| Monday | Penn State University | 2:10pm - 3:00pm in SC1320 | |||
| April 22 | Paul Baum | K-theory and K-homology | |||
| Tuesday | Penn State University | 4:10pm - 5:00pm in SC1431 | |||
| April 23 | Paul Baum | The universal example for proper actions | |||
| Wednesday | Penn State University | 2:10pm - 3:00pm in SC1320 | |||
| April 24 | Paul Baum | K-theory for group C*-algebras | |||
| Thursday | Penn State University | 1:10pm - 2:00pm in SC1214 | |||
| Shanks workshop lectures: | |||||
| May 15 | Jason Behrstock | The geometry of mapping class groups I | |||
| Thursday | Columbia University | 2pm - 3pm in SC1307 | |||
| May 16 | Jason Behrstock | The geometry of mapping class groups II | |||
| Friday | Columbia University | 2pm - 3pm in SC1307 | |||