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| Monday 17 |
3:10-4 pm, room 1432. Graph Theory and Combinatorics Seminar. Molly Dunkum, Western Kentucky University.
Destroying cycles in digraphs. For a simple directed graph G, let beta(G) be the size of the smallest subset X in E(G) so that GX has no directed cycles, and let gamma(G) denote the number of unordered pairs of nonadjacent vertices in G. Chudnovsky, Seymour, and Sullivan showed that beta(G) <= gamma(G), and conjectured that beta(G) <= gamma(G)/2. We prove that beta(G) < 0.88 gamma(G). This is joint work with Peter Hamburger and Attila P'or, Department of Mathematics and Computer Science, Western Kentucky University.
4:10-5 pm, room 1432. NCGOA Research Training Group Seminar. Dapeng Zhou, Vanderbilt University. Relative K-Theory and exact sequences. |
| Tuesday 18 |
3:20 pm, room 1425. Graduate Student Tea.
4:10-5 pm, room 1432. Noncommutative Geometry Seminar. Ziga Virk (University of Tennessee - Knoxville) Realizations of Countable Groups as Fundamental Groups of Compacta. We prove that every countable group can be realized as the fundamental group of a path connected compact subspace of four-dimensional Euclidean space. According to theorem of Shelah such space can not be locally path connected if the group is not finitely generated. This constructions complements realization of groups in the context of compact Hausdorff spaces, that was studied by Keesling, Rudyak and Przezdziecki. 4:10-5:00 pm, room 1312. Computational Analysis Seminar. Jeff Hogan, University of Arkansas. Clifford analysis and hypercomplex signal processing. In this talk we attempt to synthesize recent progress made in the mathematical and electrical engineering communities on topics in Clifford analysis and the processing of color images (for example), in particular the construction and application of Clifford-Fourier transforms designed to treat vector-valued signals. Emphasis will be placed on the two-dimensional setting where the appropriate underlying Clifford algebra is the set of quaternions. We'll conclude with some results and problems in the construction of discrete wavelet bases for color images, and the difficulties encountered in constructing the correct Fourier kernels in dimensions 3 and higher. (This talk is part of the Shanks workshop `Nonlinear Models in Sampling Theory'.) 4:30-5:30 pm, room 1308. Universal Algebra and Logic Seminar. Ralph McKenzie, Vanderbilt University. The complexity of constraint satisfaction problems: classifying the complexity of CSP problems using finite algebras III. 7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Tara Davis, Vanderbilt University. To infinity and beyond! Infinity is a universal idea that has captured man's imagination for centuries. It is ubiquitous in mathematics, art, philosophy and science. But what is infinity? We will discuss this question through the framework of history, anthropology, and mathematics, and along the way will meet some challenging questions which will illuminate just how mystical infinity really is. |
| Wednesday 19 | 4:10 pm, room 1310. Topology & Group Theory Seminar. Dan Ramras, Vanderbilt University. Gauge theory and homotopical representation theory. To every representation rho: Gamma --> G of a discrete group Gamma into a Lie group G, there is an associated map of classifying spaces Brho: BGamma --> BG, which classifies the G-bundle associated to rho. This correspondence in fact defines a continuous map B out of the representation variety Hom(Gamma, G). When Gamma admits a compact manifold as its classifying space, the homotopy fiber of this map can be interpreted using gauge theory. I'll explain this result and some of its consequences. In particular, I'll describe a calculation (up to homotopy) of the stable moduli space Hom(pi S, U)/U, where S is a surface and U is the infinite unitary group. |
| Thursday 20 | |
| Friday 21 | 4:10-5:30 pm, room 1310. Subfactor Seminar. Ionut Chifan, UC Los Angeles. Deformation/spectral gap rigidity principle for von Neumann algebras and some applications to ergodic theory. In this talk I will discuss Popa's deformation/spectral gap rigidity technique for von Neumann algebras and I will present some new applications to solidity and to ergodic theory. For instance, I will prove the folowing result: Suppose that G curvearrowright [0,1]^G is the Bernoulli action of a countable infinite group G and denote by R_{G curvearrowright [0,1]^G} the induced equivalence relation. Then for every subequivalence relation S subset R_{G curvearrowright [0,1]^G} there exists a measurable partition {X_i}, i geq 0 of [0,1]^G formed of R-invariant sets such that R_{-X_0} is hyperfinite and R_{-X_i} is strongly ergodic (hence non-hyperfinite and ergodic) for every i geq 1. This talk is based on two papers I have written jointly with A. Ioana respectively C. Houdayer. pdf version |