Rice University Math Department Calendar

    September 2009          October 2009          November 2009    
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
        1  2  3  4  5                1  2  3    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    4  5  6  7  8  9 10    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   11 12 13 14 15 16 17   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   18 19 20 21 22 23 24   22 23 24 25 26 27 28
 27 28 29 30            25 26 27 28 29 30 31   29 30

2:30 pm Thursday, October 15, 2009
Current Math Seminar: Introduction to Contact Homology
by Bridget D Franklin (Rice University) in HB 227

Contact Homology, one specialized version of Floer Homology, is currently a very active area of research in Topology. In this talk, I will be following notes of a talk given by John Etnyre at the 2009 GITC as well as discussing some of what I learned at the MSRI Workshop in Symplectic and Contact Geometry and Topology. I will give a general discussion Contact Homology which studies the properties of M, a compact, oriented, 2n-1 dimensional manifold endowed with a contact structure. I will specialize this to the discussion of Legendrian Contact Homology which gives an invariant of Legendrian submanifolds of M, which is useful in the study of the isotopy classes of Legendrian knots in R^3 given the standard contact structure. If time permits, we will look at relationships between Contact Homology and other Floer Homology Theories.Host Department: Rice University-Mathematics
Submitted by sm29@rice.edu

4:00 pm Thursday, October 15, 2009
Colloquium: Dirichlet’s theorem on Diophantine approximation and
by Nimish A. Shah (The Ohio State University) in HB 227

In the late sixties, Baker and Schmidt proved that Dirichlet’s theorem on simultaneous Diophantine approximation of n real numbers x_1,...,x_n$ cannot be improved in a certain precise sense for almost all (x_1,...,x_n) in R^n. Answering a question asked by them, we show that the non-improvability result also holds for almost all points on any analytic curve in R^n which is not contained in a proper affine subspace. The problem is reformulated in terms of a dynamical question on homogeneous spaces which is then resolved by proving a new equidistribution theorem for on the space of unimodular lattices in R^{n+1}. The proof involves Ratner's theorem on unipotent flows and linearization technique. Host Department: Rice University-Mathematics
Submitted by dani@rice.edu