Seminars and Colloquia by Series

Wednesday, April 8, 2009 - 12:00 , Location: Skiles 255 , Hao Min Zhou , School of Mathematics, Georgia Tech , Organizer:
This talk will be a continuation of the one I gave in this Seminar on March~11. I will present a brief introduction to use partial differential equations (PDE) and variational techniques (including techniques developed in computational fluid dynamics (CFD)) into wavelet transforms and Applications in Image Processing. Two different approaches are used as examples. One is PDE and variational frameworks for image reconstruction. The other one is an adaptive ENO wavelet transform designed by using ideas from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing.
Wednesday, March 11, 2009 - 12:00 , Location: Skiles 255 , Hao Min Zhou , School of Mathematics, Georgia Tech , Organizer:
In this talk, I will present an brief introdution to use partial differential equation (PDE) and variational techniques (including techniques developed in computational fluid dynamics (CFD)) into wavelet transforms and Applications in Image Processing. Two different approaches are used as examples. One is PDE and variational frameworks for image reconstruction. The other one is an adaptive ENO wavelet transform designed by using ideas from Essentially Non-Oscillatory (ENO) schemes for numerical shock capturing.
Wednesday, February 25, 2009 - 12:00 , Location: Skiles 255 , Federico Bonetto , School of Mathematics, Georgia Tech , Organizer:
I'll give a brief introduction to the to Quantum Statistical Mechanics in the case of systems of Fermions (e.g. electrons) and try to show that a lot of the mathematical problems can be framed in term of counting (Feynman) graphs or estimating large determinants.
Wednesday, February 18, 2009 - 12:00 , Location: Skiles 255 , Matt Baker , School of Mathematics, Georgia Tech , Organizer:
I will give a modern bijective proof of Kirchhoff's classical theorem relating the number of spanning trees in a graph to the Laplacian matrix of the graph. The proof will highlight some analogies between graph theory and algebraic geometry.
Wednesday, February 11, 2009 - 12:00 , Location: Skiles 255 , Wing Suet Li , School of Mathematics, Georgia Tech , Organizer:
The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The original proof by Klyachko and Knutson-Tao, requires tools from algebraic geometry, among other things. Our recent work provides a proof using only elementary tools that made it possible to generalize the Horn inequalities to finite von Neumann factors. No knowledge of von Neumann algebra is required.
Wednesday, February 4, 2009 - 12:00 , Location: Skiles 255 , Sinem Celik Onaran , Department of Mathematics, Middle East Technical University , Organizer:
Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will define open book decompositions of 3-manifolds. We will discuss various examples and sketch the proof of Alexander's theorem. Further, we will discuss the importance of the open books in manifold theory, in particular in contact geometry.
Wednesday, January 28, 2009 - 12:00 , Location: Skiles 255 , Antoine Henrot , University of Nancy, France , Organizer:
In this talk, we give an insight into the mathematical topic of shape optimization. First, we give several examples of problems, some of them are purely academic and some have an industrial origin. Then, we look at the different mathematical questions arising in shape optimization. To prove the existence of a solution, we need some topology on the set of domains, together with good compactness and continuity properties. Studying the regularity and the geometric properties of a minimizer requires tools from classical analysis, like symmetrization. To be able to define the optimality conditions, we introduce the notion of derivative with respect to the domain. At last, we give some ideas of the different numerical methods used to compute a possible solution.
Wednesday, January 14, 2009 - 12:00 , Location: Skiles 255 , Stavros Garoufalidis , School of Mathematics, Georgia Tech , Organizer:
The Apery sequence is a sequence of natural numbers 1,5,73,1445,...which is used to prove the irrationality of zeta(3). Can you compute its asymptotic expansion to all orders of 1/n? The talk will not assume a lot, but promises to compute, and also justify.
Wednesday, November 19, 2008 - 12:00 , Location: Skiles 255 , Silas Alben , School of Mathematics, Georgia Tech , Organizer:
We examine some problems in the coupled motions of fluids and flexible solid bodies. We first present some basic equations in fluid dynamics and solid mechanics, and then show some recent asymptotic results and numerical simulations. No prior experience with fluid dynamics is necessary.
Tuesday, November 4, 2008 - 12:00 , Location: Skiles 255 , Doron Lubinsky , School of Mathematics, Georgia Tech , Organizer:
Orthogonal polynomials play a role in myriads of problems ranging from approximation theory to random matrices and signal processing. Generalizations of orthogonal polynomials - such as biorthogonal polynomials, cardinal series, Muntz polynomials, are used for example, in number theory and numerical analysis. We discuss some of these, and some potential research projects involving them.

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