Rice University Math Department Calendar

      March 2011             April 2011              May 2011      
 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    1  2  3  4  5  6  7
  6  7  8  9 10 11 12    3  4  5  6  7  8  9    8  9 10 11 12 13 14
 13 14 15 16 17 18 19   10 11 12 13 14 15 16   15 16 17 18 19 20 21
 20 21 22 23 24 25 26   17 18 19 20 21 22 23   22 23 24 25 26 27 28
 27 28 29 30 31         24 25 26 27 28 29 30   29 30 31

12:00 pm Friday, April 8, 2011
Stulken Geometry-Analysis Seminar: Second order rectifiability of integral varifolds of locally bounded first variation
by Ulrich Menne [mail] (Max-Planck-Institut für Gravitationsphysik) in HB 427

Consider singular submanifolds of Euclidean space admitting a generalized mean curvature. It is shown that this condition entails the existence of a second order structure. The proof uses approximation by Almgren's multiple-valued functions and a new differentiability result for Laplace's operator.Host Department: Rice University-Mathematics
Submitted by lr7@rice.edu

4:00 pm Friday, April 8, 2011
Stulken Geometry-Analysis Seminar: Universality of transitions at the point of gradient catastrophe for some integrable systems and some orthogonal polynomials
by Alexander Tovbis [mail] (University of Central Florida) in HB 227

By a point of gradient catastrophe we mean a point where the leading order asymptotic behavior loses smoothness (for example, derivatives are not square integrable). In the case of the small dispersion (semiclassical) focusing NLS, this is a point where a slowly modulated high frequency plane wave wave suddenly burst into rapid amplitudial oscillation (spikes). Adjusting the nonlinear steepest descent (Deift-Zhou) method for Riemann-Hilbert problems, we give complete description of the leading order term near the point of gradient catastrophe in terms the {\em tritronqu\'ee} solution to the Painlev\'e I and rational breathers for the NLS. In fact, each spike corresponds to a pole of the {\em tritronqu\'ee} and has the universal shape shape of a scaled rational breather. Similar phenomenon was recently described for the asymptotic of orthogonal polynomials with complex varying weight $e^{-N (\hf z^2 + \qt t z^4)}$ near the critical value of the parameter $t$. In this case the spikes in the asymptotics for the recurrence coefficients turn out to be bounded for $t\in\R$ but unbounded for complex $t$.Host Department: Rice University-Mathematics
Submitted by belov@rice.edu

4:00 pm Friday, April 8, 2011
Thesis Defense: The (n)-solvable filtration of the link concordance group and Milnor's μ-invariants
by Carolyn Otto (Rice University) in HB 427

F ^m_n

C^m

F ^m_n.5 / F ^m_n+1

G ^m_n

C^m

Host Department: Rice University-Mathematics
Submitted by mathweb@rice.edu