Seminars and Colloquia by Series

High order numerical methods for differential equations with singular sources

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 19, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Jae-Hun Jung – Mathematics, SUNY Buffalo
Solutions of differential equations with singular source terms easily becomenon-smooth or even discontinuous. High order approximations of suchsolutions yield the Gibbs phenomenon. This results in the deterioration ofhigh order accuracy. If the problem is nonlinear and time-dependent it mayalso destroy the stability. In this presentation, we focus on thedevelopment of high order methods to obtain high order accuracy rather thanregularization methods. Regularization yields a good stability condition,but may lose the desired accuracy. We explain how high order collocationmethods can be used to enhance accuracy, for which we will adopt severalmethods including the Green’s function approach and the polynomial chaosmethod. We also present numerical issues associated with the collocationmethods. Numerical results will be presented for some differential equationsincluding the nonlinear sine-Gordon equation and the Zerilli equation.

Test - RT 159125

Series
Other Talks
Time
Saturday, April 17, 2010 - 13:07 for 4 hours (half day)
Location
158
Speaker
All Around Nice Guy – Buddy and Pal –
Abstract expressionism is a post–World War II art movement in American painting, developed in New York in the 1940s. It was the first specifically American movement to achieve international influence and put New York City at the center of the western art world, a role formerly filled by Paris.

The Faber-Krahn problem for the Hamming cube

Series
Combinatorics Seminar
Time
Friday, April 16, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Alex Samordnitsky – Professor, Hebrew University (Jerusalem, Israel)
The Faber-Krahn problem for the cube deals with understanding the function, Lambda(t) = the maximal eigenvalue of an induced t-vertex subgraph of the cube (maximum over all such subgraphs). We will describe bounds on Lambda(t), discuss connections to isoperimetry and coding theory, and present some conjectures.

Cohomological equations on dynamical systems arising from Delone sets.

Series
Math Physics Seminar
Time
Thursday, April 15, 2010 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dr Alvaro Daniel Coronel – Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Santiago, Chile –

Please Note: The speaker is visiting Georgia Tech for the full week. His office will be Skiles 133A.

This talk concerns aperiodic repetitive Delone sets and the dynamical systems associated with them. A typical example of an aperiodic repetitive Delone set is given by the set of vertices of the Penrose tiling. We show that natural questions concerning aperiodic repetitive Delone sets are reduced to the study of some cohomological equations on the associated dynamical systems. Using the formalism of tower systems introduced by Bellissard, Benedetti, and Gambaudo, we will study the problem about the existence of solution of these cohomological equations.

Tangent cones and regularity of real hypersurfaces

Series
Analysis Seminar
Time
Wednesday, April 14, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mohammad Ghomi – Georgia Tech
The tangent cone of a set X in R^n at a point p of X is the limit of all rays which emanate from p and pass through sequences of points p_i of X as p_i converges to p. In this talk we discuss how C^1 regular hypersurfaces of R^n may be characterized in terms of their tangent cones. Further using the real nullstellensatz we prove that convex real analytic hypersurfaces are C^1, and will also discuss some applications to real algebraic geometry.

BILLIARDS-the most visual dynamical systems (from ORDER to CHAOS and COMPLEXITY)

Series
ACO Student Seminar
Time
Wednesday, April 14, 2010 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Prof. Leonid Bunimovich – School of Mathematics, Georgia Tech
Billiards is a dynamical system generated by an uniform motion of a point particle (ray of light, sound, etc.) in a domain with piecewise smooth boundary. Upon reaching the boundary the particle reflected according to the law "the angle of incidence equals the angle of reflection". Billiards appear as natural models in various branches of physics. More recently this type of models were used in oceanography, operations research, computer science, etc. I'll explain on very simple examples what is a regular and what is chaotic dynamics, the mechanisms of chaos and natural measures of complexity in dynamical systems. The talk will be accessible to undergraduates.

Athens/Atlanta Number Theory Seminar - Lecture 1 - Degree three cohomology of function fields of surfaces

Series
Other Talks
Time
Tuesday, April 13, 2010 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Venapally Suresh – University of Hyderabad / Emory University
Let k be a global field or a local field. Class field theory says that every central division algebra over k is cyclic. Let l be a prime not equal to the characteristic of k. If k contains a primitive l-th root of unity, then this leads to the fact that every element in H^2(k, µ_l ) is a symbol. A natural question is a higher dimensional analogue of this result: Let F be a function field in one variable over k which contains a primitive l-th root of unity. Is every element in H^3(F, µ_l ) a symbol? In this talk we answer this question in affirmative for k a p-adic field or a global field of positive characteristic. The main tool is a certain local global principle for elements of H^3(F, µ_l ) in terms of symbols in H^2(F µ_l ). We also show that this local-global principle is equivalent to the vanishing of certain unramified cohomology groups of 3-folds over finite fields.

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