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WEEKLY CALENDAR |
| Monday 8 | |
| Tuesday 9 |
4:10-5:30 pm, room 1308. Universal
Algebra
and Logic Seminar. Organizational Meeting.
4:10-5:00 pm, room 1312. Computational Analysis Seminar. Larry Schumaker, Vanderbilt University. Dimension of Spline Spaces on T-Meshes. A T-mesh $\Delta$ is obtained from a tensor-product mesh by removing certain edges to create a partition with one or more T-nodes. Given $0 \le r_1 \le d_1$ and $0 \le r_2 \le d_2$, we define an associated spline space $S^{r_1,r_2}_{d_1,d_2}(\Delta)$ as the space of functions in $C^{r_1,r_2}$ whose restrictions to the rectangles of the partition are tensor polynomials in $P_{d_1,d_2}$. In this talk we discuss the problem of computing the dimension of these spline spaces. In particular, we give various lower bounds which lead to exact formulae in some cases. We also discuss extensions to more than two variables, and also some results for more general L-meshes. Finally, we conclude with several enticing open questions. 4:10-5:15 pm, room 1432. Noncommutative Geometry Seminar. Romain Tessera, Vanderbilt University. The stable Borel conjecture for linear groups. Inspired by the notion of asymptotic dimension, we will introduce a more flexible large-scale geometric property of a group called Finite Decomposition Complexity. This property will be proved for a large class of groups such as all subgroups of GL_n(A) where A is a commutative ring. On the other hand, this property being shaped for "cutting and pasting" methods, we show that if a group has Finite Decomposition Complexity, then it satisfies the Novikov and the stable Borel conjecture. |
| Wednesday 10 | 4:10 pm, room 1310. Topology & Group Theory Seminar. David Ayala, Stanford University. Stable Automorphism Groups of Locally Defined Objects. There are numerous classes of groups which are naturally represented as the automorphism groups of (locally defined) geometric objects. Examples include symmetric groups, automorphism groups of free groups, braid groups, and mapping class groups of surfaces. These examples all have an obvious notion of stabilization by increasing the number of letters, strands, or genus. I will begin this talk by indicating how to make sense of 'stabilizing' the classifying spaces of such classes of groups in general. I will then outline a general procedure for identifying the homotopy type of this stabilized classifying space. I will finish by pointing out applications to the groups mentioned above and also to the theory of holomorphic curves. The work I will discuss is inspired by techniques of Galatius and follows the recent ideas in cobordism theory due to Madsen, Weiss, Galatius, and Tillmann. |
| Thursday 11 | |
| Friday 12 |
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Glenn Webb, Vanderbilt University. Analysis of a model for transfer phenomena in biological populations. The problem of transfer in a population structured by a continuous quantity is analyzed. The transfer of the quantity occurs between individuals according to specified rules. The simple model is an ordinary differential equation in the Banach space of integrable functions, of Boltzmann type with kernel corresponding to a transfer process. It is proved that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. The simple model is generalized by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that the transfer rate is sufficiently small. An application is made to a model of proliferating cell populations with individual cells exchangimg the surface protein P-glycoprotein, which plays an important role in acquired multidrug resistance against cancer chemotherapy.
4:10-5:30 pm, room 1310. Subfactor Seminar. Romain Tessera, Vanderbilt University. A characterization of relative property T (joint work with Yves de Cornulier). We prove that a semidirect product of a group G with an abelian group V does not have relative property T with respect to V if and only if there exists a mean on the dual of V, which is: G-invariant; supported on the trivial representation; and distinct from the dirac measure. |