 |
WEEKLY CALENDAR |
| Monday 15 | 3:10 pm, room 1432. Graph Theory and Combinatorics Seminar. Matjaz Konvalinka. Combinatorics of determinantal identities. In this talk, we apply combinatorial means for proving and generalizing classical determinantal identities. We start with the construction of a fundamental bijection between certain monomials; this proves crucial for most of the results that follow. We continue with the first, and possibly the best-known, determinantal identity, the matrix inverse formula, both in the commutative case and in some non-commutative settings (Cartier-Foata variables, right-quantum variables, and their weighted generalizations). The next part is dedicated to the celebrated MacMahon master theorem and Sylvester's determinantal identity; we present their generalizations and applications. The last part has a slightly different, representation theory flavor; it involves representations of the symmetric group, and also Hecke algebras and their characters. We extend a result on immanants due to Goulden and Jackson to a quantum setting, and reprove certain combinatorial interpretations of the characters of Hecke algebras due to Ram and Remmel. |
| Tuesday 16 |
4:10 pm, Wilson Hall 103. A&S Faculty Meeting. Reception following.
4:10-5 pm, room 1432. Joint Topology, Group Theory, and Noncommutative Geometry Seminar. Christophe Pittet, University of Marseille. Bounded 2-cocycles on Lie groups. Characteristic numbers of flat principal bundles admit universal bounds if the structural group is algebraic. This was first discovered by Milnor for SL(2,R) then generalized by Gromov and others to all algebraic groups. We show that the algebraic condition can be weakened. This is joint work with Chatterji, Mislin, Saloff- Coste. 4:10-5:00 pm, room 1312. Computational Analysis Seminar. Hendrik Speleers, Katholieke Universiteit Leuven. From PS splines to QHPS splines. Powell-Sabin (PS) splines are C1-continuous quadratic macro-elements defined on conforming triangulations. They can be represented in a compact normalized spline basis with a geometrically intuitive interpretation involving control triangles. These triangles can be used to interactively change the shape of a PS spline in a predictable way. In this talk we discuss a hierarchical extension of PS splines, the so-called quasi-hierarchical Powell-Sabin (QHPS) splines. They are defined on a hierarchical triangulation obtained through (local) triadic refinement. For this spline space a compact normalized quasi-hierarchical basis can be constructed. Such a basis retains the advantages of the PS spline basis: the basis functions have a local support, they form a convex partition of unity, and control triangles can be defined. In addition, they admit local subdivision in a very natural way. These properties of QHPS splines are appropriate for local adaptive approximation and modelling. 4:30-5:50 pm, room 1308. Universal Algebra and Logic Seminar. Matthew Nickodemus, Vanderbilt University. The Stone Duality Theorem. In 1936, Marshall Stone proved that every Boolean algebra is isomorphic to the algebra of all clopen subsets of some totally disconnected compact space. In this talk, I will prove Stone's Theorem. My talk will be aimed at first year graduate students, and advanced undergraduates. |
| Wednesday 17 | 4:10 pm, room 1310. Topology & Group Theory Seminar. Tom Baird, Oxford University. Moduli spaces of flat bundles over nonorientable surfaces. Moduli spaces of flat bundles over orientable surfaces have been actively studied for many years. They have wide ranging applications in such diverse fields as algebraic geometry, low dimensional topology and mathematical physics. Moduli spaces of flat bundles over nonorientable surfaces have received less scrutiny, and have recently been shown to possess interesting geometric and topological properties. For rank 2 bundles the topology is well understood and I will begin my lecture by describing this case. I will then provide a conjectural description of the higher rank case and detail efforts to prove this conjecture. |
| Thursday 18 | |
| Friday 19 |
4:10-5:30 pm, room 1310.
Subfactor Seminar. Pinhas Grossman, Vanderbilt University. Strong Singularity for Subfactors. We will describe an example of a subfactor of the hyperfinite II1 factor which is singular but not strongly singular (with constant one). This is joint work with Alan Wiggins.
4:10-5:00 pm, room 1307. Partial Differential Equations Seminar. Gieri Simonett, Vanderbilt University. On normal stability for nonlinear parabolic equations. We study convergence of solutions for quasilinear and fully nonlinear parabolic evolution equations in situations where the set of equilibria is non-dicrete, but forms a C1-manifold which is normally stable. Our approach uses tools from the theory of maximal regularity in an essential way. |