Seminars and Colloquiums
for 2010-2011
Week of April 18, 2011
Speaker:
Mr. Joe Hughes, Tuesday
Professor Steve Wise, Wednesday
Professor Mrinal Raghupathi, Vanderbilt University, Wednesday
Professor Pengzi Miao, University of Miami , Thursday
If you are interested in giving or arranging a talk for one of our seminars or colloquiums,
please review our calendar.
If you have questions, or a date you would like to confirm, please contact Dr. Fernando Schwartz.
Tuesday, April 19
MATH BIOLOGY SEMINAR
TIME: 9:45 – 10:45 a.m.
ROOM: NIMBioS Classroom
SPEAKER: Joe Hughes
TITLE: "Biological Applications of Stochastic Differential Equations"
Wednesday, April 20
APPLIED/COMPUTATIONAL MATH SEMINAR
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 111
SPEAKER: Professor Steve Wise
TITLE: "Multigrid Methods and Convergence", Part 3 of 3
ABSTRACT: Multigrid solvers are optimal order iterative solvers for a class of linear (and weakly nonlinear) equations resulting from the discretization of elliptic and elliptic-like PDEs. In the best case,
the amount of work to obtain a "solution" is on the order of N, where N represents the total number of unknowns (i.e., the dimension of the solution vector). Compare this with the work required for Gaussian elimination. In this series I will describe the methods in some detail, giving an intuitive explanation of why the methods are so efficient and describing modifications for nonlinear problems and the adaptive setting. The convergence proofs will be for the simplest cases in the finite difference and finite element frameworks. The prerequisites are modest, advanced calculus and advanced linear algebra should suffice.
ANALYSIS SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres 114
SPEAKER: Professor Mrinal Raghupathi, Vanderbilt University
TITLE: "Tangential interpolation for subalgebras of Pick spaces"
ABSTRACT: This is joint work with Ryan Hamilton. Three classical theorems in function theory and operator theory are the pick interpolation problem, and its tangential variant; the problem of
interpolating sequences; and the corona problem. I will present some of the background to these problems.
I will then present some motivation for the study of function theory in subalgebras of $H^\infty$ and prior results obtained with Brett Wick. I will then sketch a tangential interpolation result for
subalgebras of a complete Pick space that makes use of property $A_1(1)$.
Thursday, April 21
COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Professor Pengzi Miao, University of Miami
TITLE: Research on boundary geometry of compact manifolds via the positive mass theorem
ABSTRACT: The positive mass theorem, originating from Einstein's theory of general relativity, has been proven to be a useful tool in differential geometry over the past three decades. Since its first establishment by Schoen and Yau in 1979, the theorem has been used to solve many important
geometric problems, among which the most notable ones are Schoen's resolution of the Yamabe conjecture and Bray's proof of the Riemannian Penrose inequality.
In the past ten years, there has been a new trend emerging in the application of the positive mass theorem. It started with Shi and Tam's remarkable work on proving the positivity of Brown-York mass, which is tied to the quasi-local mass question in general relativity. From a geometric perspective, the idea here is to apply the positive mass theorem to study the boundary geometry of compact manifolds with nonnegative scalar curvature. In this talk, we give a brief survey of results motivated by this idea.
Please join us for refreshments at 3:15 p.m.
Past notices:
winter break
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year