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| Monday 29 | 3:10-4 pm, room 1432. Graph Theory and Combinatorics Seminar. Mark Ellingham, Vanderbilt University. Embedding complete tripartite graphs. For several years the speaker, with Chris Stephens and Xiaoya Zha, has been working on determining the orientable genus of complete tripartite graphs. In this talk we describe the techniques used, including diamond sums to construct embeddings from smaller embeddings, transition graphs to construct embeddings algebraically, and vertex duplication to modify surfaces to allow more vertices to be added to a graph. As an example, we will show how to put all of this together to embed K_{1002,11,8} on the 4250-holed torus. |
| Tuesday 30 |
3:20 pm, room 1425. Graduate Student Tea.
4:10-5 pm, room 1432. Noncommutative Geometry Seminar. Jesse Peterson, Vanderbilt University. A remark on Popa's HT factors. If $\Gamma$ is a discrete group with the Haagerup property and $\Gamma$ acts freely and ergodically on a standard probability space $(X, \mu)$, then Popa showed that $L^\infty(X, \mu)$ is the only possible rigid Cartan subalgebra of $N = L^\infty(X, \mu) \rtimes \Gamma$. We will explain these results and some consequences using derivations on the von Neumann algebra $N$. This setting will allow us to generalize Popa's result to include a larger class of groups, e.g. groups with positive first $\ell^2$-Betti number. 4:30-5:30 pm, room 1308. Universal Algebra and Logic Seminar. Petar Markovic, University of Novi Sad, Serbia. An Idiot's Guide to Complexity I. I will attempt to give the basic concepts, ideas and results of the theory of computational complexity. The lecture is geared towards first-year graduate students and people who may have heard these notions before but never in a systematic way. 7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Justin Fitzpatrick, Vanderbilt University. To Deal or Not to Deal, That is the Question. Getting on a game show is a once-in-a-lifetime opportunity, so you had better go prepared! In this talk, we will prepare you specifically to play correctly on the wildly popular game shows "Deal or No Deal" and "The Price is Right." We introduce the concept of expected value, a concept that is extremely integral to determining correct strategy for many games, and then apply it and other game-theoretic concepts to these two game shows. You will learn when to deal, when not to deal, when to spin again, and when to let the next person spin! And, since there is no substitute for experience, we will allow four lucky students to COME ON DOWN and compete for prizes!! Free pizza. |
| Wednesday 1 | 4:10 pm, room 1310. Topology & Group Theory Seminar. Alvaro Martinez-Perez, Universidad Complutense de Madrid. A characterization of quasi-isometry between R-trees. One of the possible strategies to study the quasi-isometry type of a metric hyperbolic space is to look at its border or end space. In this sense, F. Paulin proves that if the isometry groups of hyperbolic metric spaces have a certain property, then quasi-isometries between the spaces can be characterized by a condition on the induced homeomorphism between the end spaces. In this talk, we present an intrinsic characterization of quasi-isometry between R-trees based on a new condition on the induced homeomorphism between their ends. This is a joint work with M. A. Moron and B. Hughes. |
| Thursday 2 | 4:10-5 pm, room 5211. Colloquium. Kenneth Davidson, University of Waterloo, Canada. Topological stable rank of Banach algebras. 25 years ago, Rieffel introduced an algebraic invariant for Banach algebras called topological stable rank which generalized the notion of dimension to the non-commutative setting. The topological stable rank has a left and right version, which coincide for C*-algebras and commutative algebras. Moreover, tsr is a Banach algebra variant of the purely algebraic invariant of Bass stable rank for rings-and the left and right versions of Bass stable rank are always equal. So Rieffel asked whether they are always equal? We have calculated the left and right topological stable ranks for the class of nest algebras, and can answer Rieffel's question negatively. Tea at 3:30 pm in SC 1425. |
| Friday 3 | 4:10-5:30 pm, room 1310. Subfactor Seminar. Shamindra Ghosh, Vanderbilt University. From planar algebras to subfactors. Starting from a planar algebra satisfying suitable conditions, we will describe the construction (by Jones, Shlyakhtenko and Walker) of a subfactor whose planar algebra is the one with which we started. The first construction was given by Popa, and then by Guionnet, Shlykhtenko and Jones. |
| Saturday 4 | |
| Sunday 5 | 2-7 pm. Department Picnic. Edwin Warner Park Area #5 (NOTE: This is a different area from last year). A map of the park is at www.nashville.gov/parks/locations/warner.htm. Please RSVP by October 1 to Justin Schroeder (justin.z.schroeder@vanderbilt.edu) and let him know how many will be attending and what kind of side dish or dessert you are bringing. There will be fun and games for all, so bring your family and friends! |