WEEKLY  CALENDAR
November 2006
Vanderbilt Mathematics

 

Monday 6

12:10-1 pm, room 1404. Graph Theory and Combinatorics Seminar. Mike Plummer, Vanderbilt University. On the matching extendability of graphs in surfaces. A graph G with at least 2n+2 vertices is said to be n-extendable if every matching of size n in G extends to a perfect matching. It is shown that (1) if a graph is embedded on a surface of Euler characteristic chi, and the number of vertices in G is large enough, the graph is not 4-extendable; (2) given g > 0, there are infinitely many graphs of orientable genus g which are 3-extendable, and given g' >= 2, there are infinitely many graphs of non-orientable genus g' which are 3-extendable; and (3) if G is a 5-connected triangulation with an even number of vertices which has genus g and sufficiently large representativity, then it is 2-extendable. This is joint work with R.E.L. Aldred of Otago University, Dunedin, New Zealand and Ken-ichi Kawarabayashi of the National Institute for Informatics, Tokyo, Japan.

4:10-5:30 pm, room 1310. Subfactor Seminar. Pinhas Grossman, Vanderbilt University. Indices and angles for supertransitive intermediate subfactors.

4:10-5:30 pm, room 1312. Universal Algebra and Logic Seminar. Wieslaw Dziobiak, University of Puerto Rico, Mayaguez. Endomorphisms of Monadic Boolean Algebras. A classical result about Boolean algebras -- independently proved by Magill, Maxson, and Schein -- states that non-trivial Boolean algebras are isomorphic whenever their endomorphism monoids are isomorphic. The main point of this talk is to show that the finite part of this classical result is true within monadic Boolean algebras. By contrast, there exists a proper class of non-isomorphic (necessarily) infinite monadic Boolean algebras the endomorphism monoid of each of which has only one element (namely, the identity map). [Joint work with M.E. Adams (SUNY)]

Tuesday 7

4 pm, room 1310. Computational Analysis Seminar. Darrin Speegle, St. Louis University. The Feichtinger Conjecture for special classes of frames. Feichtinger conjectured that every frame for a Hilbert space can be partitioned into the finite union of sets, each of which is a Riesz basis for its closed linear span. It was quickly realized that this conjecture was closely related to the paving problem for matrices, and thus to the Kadison-Singer problem. More recently, it has been shown that settling the Feichtinger Conjecture is equivalent to solving the paving problem. In this talk I will review the partial results on the paving problem, primarily by Bourgain and Tzafriri, and translate them into partial results on the Feichtinger Conjecture. Then, I will describe the progress that has been made for Gabor frames, wavelet frames and frames of exponentials. For these restricted classes of frames, it is not clear whether settling the Feichtinger Conjecture is equivalent to solving the corresponding paving problems. Despite progress, the Feichtinger Conjecture remains open even in this restricted setting.

4:10-5 pm in room 1432. Noncommutative Geometry Seminar. Thomas Sinclair, Vanderbilt University. Introduction to Homology of Groups and Algebras. The talk will begin with a brief but "gentle" introduction of basic homological algebra, after which the talk will specialize to the cases of Group Homology and Hochschild Homology for Algebras. The motivating result for the talk will be the fact that the homology of a group agrees with the Hochschild homology of its complex group algebra. This connection lies at the core of the Noncommutative Differential Geometry of Connes as well as the theory of L^2-Betti numbers for von Neumann algebras as developed by Connes-Shlyakhtenko.

7-8 pm, room 1206. Undergraduate Seminar in Mathematics. Fumiko Futamura, Vanderbilt University. TBA.

Wednesday 8

3:10 pm, room 1310. Analysis & Biomathematics Seminar. Anne Kenworthy, Vanderbilt University. Modeling intracellular transport and membrane domain structure in living cells. We are interested in the fundamental processes that cells use to target membrane proteins to their correct intracellular destination, as well as how the lateral organization of proteins within cell membranes impacts their function. I will discuss two ongoing projects in the lab that use a combination of quantitative fluorescence microscopy-based approaches and mathematical modeling to address these issues. The first uses kinetic analysis to investigate the mechanism of binding of Ras, a protein often mutated in human tumors, to intracellular membranes. This work relies mainly on the use of partial differential equations to model protein diffusion and membrane binding via either a partitioning or receptor-mediated mechanism. The second uses a Monte Carlo approach to simulate a technique known as FRET that reports on the inter-molecular distances of fluorescently-tagged molecules. This study addresses the problem of how data on inter-molecular distances from FRET can be used to study the two-dimensional spatial organization of proteins in membranes.

3:30-4:30 pm, room 1425. Graduate student tea. All math personnel are invited.

4:10-5 pm, room 1310. Topology & Group Theory Seminar will not meet this week.

4:10- 5 pm, room 1308. Special Lecture. Yuri Gurevich, Microsoft Research. Zero-one laws in discrete mathematics. The fraction of n-vertex finite graphs that are connected grows to 1 as n grows to infinity. In that sense almost all finite graphs are connected. There are numerous results like that. Almost all graphs are Hamiltonian, not 3-colorable, rigid, etc. Each of these results required a separate proof. Is there a general phenomenon behind results of that sort? It turns out that much depends on the logical form of the property in question. In particular, every claim expressible in predicate logic is almost surely true or almost surely false on finite structures. This zero-one law was generalized in various directions. We will explain some of the results.

5:30 pm, room 1425. Math Club.

Thursday 9

1:10-2 pm, room 1310. NCGOA Research Training Group Seminar. Lin Shan, Vanderbilt University. Roe Algebra.

4:10-5 pm, room SC 5211. Colloquium. Valery Alexeev, University of Georgia. Higher-dimensional analogs of stable curves. Stable curves were introduced in the 60s by Deligne-Mumford (and versions by Mayer, Knudsen, Grothendieck...). Stable maps is a more recent invention of Kontsevich. They have a myriad of applications: most notably to Gromov-Witten invariants and quantum cohomology, but also to such diverse topics as resolutions of singularities in positive characteristic and universal bounds for the number of solutions of diophantine equations. Tea at 3:30 pm in SC 1425.

Friday 10

 

In the online version of this page, all underlined phrases are links; some mathematical symbols may require a browser with symbol font. Past calendars are available, as well as next week's calendar (in preparation) and a web page listing just our colloquia. We update the online calendar whenever we get information, but generally we only print paper copies on Fridays. Please submit events as early as possible, to math.calendar@vanderbilt.edu.

Other events: