Seminars and Colloquiums
for the week of September 24, 2007
Speakers:
Dr. Cheng Wang, Monday
Dr. David Anderson, Tuesday
Professor Elias Wegert, Technical University Freiberg, Wednesday
Dr. Robert Daverman, Thursday
Dr. Rick Kenyon, Brown University, Thursday
Monday, September 24
DE/APPLIED AND COMPUTATIONAL MATH SEMINAR
TIME: 3:35-4:30 p.m.
ROOM: Ayres 309A
SPEAKER: Dr. Cheng Wang
TITLE: Fourth order finite difference time domain (FDTD) scheme of Maxwell equations
ABSTRACT: A fourth order difference scheme of Maxwell equations over a staggered Yee grid is proposed and analyzed in detail. A ``symmetric image'' extrapolation is utilized to avoid the difficulty around the boundary, and the Jameson Runge-Kutta method is chosen as the time integration. The stability condition is derived with perfectly conducting boundaries. The full fourth order convergence analysis is provided in both L2 and L^infinity norms. Numerical simulations of a benchmark cavity, single and double ridge cavities, and twisted wave guide are also discussed and presented in detail.
Tuesday, September 25
ALGEBRA SEMINAR
TIME: 2:10 p.m. - 3 p.m.
ROOM: Ayres Hall 309B
SPEAKER: Dr. David Anderson
TITLE: The D + M Construction
Wednesday, September 26
ANALYSIS SEMINAR
TIME: 3:35 p.m. - 4:25 p.m.
ROOM: Ayres Hall 209A
SPEAKER: Professor Elias Wegert, Technical University Freiberg
TITLE: Nonlinear Riemann-Hilbert Problems
Thursday, September 27
TOPOLOGY-GEOMETRY SEMINAR M669
TIME: 12:40 - 1:55 p.m.
ROOM: DO 501 (Dougherty)
SPEAKER: Dr. Robert Daverman
TITLE: Admissible subsets of wild Cantor sets
MATHEMATICS COLLOQUIUM
TIME: 3:40 p.m.
ROOM: Ayres Hall 214
SPEAKER: Dr. Rick Kenyon, Brown University
TITLE: Dimers and Random Surfaces
ABSTRACT: We study a natural family of smooth surfaces in3-space arising as limits of random discrete "stepped" surfaces. For fixed boundary conditions, the law of large numbers for stepped surfaces leads to a PDE for the limit surfaces (when the lattice spacing tends to zero). This PDE is a variant of the complex Burgers equation and can be solved analytically via holomorphic functions. This is surprising since the surfaces generically have both smooth parts and facets. The interplay between analytic (even algebraic) functions and facet formation in the surfaces leads to some interesting questions in real algebraic geometry.
Additional info:
Dr. Kenyon is known for his deep work in discrete geometry, probability, differential geometry, and for its application in physics and statistical mechanics. The topic of the lecture comes in part from joint work with Alexander Okaunkov, work which weighed heavily in Okaunkov's selection as a Field's Metalist in 2004.
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Seminars from 2006-2007 academic year