Seminars and Colloquia by Series

Alice in Wonderland learns how to compute determinants.

Series
Research Horizons Seminar
Time
Wednesday, September 23, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Stavros Garoufalidis – Georgia Tech School of Mathematics –
Dodgson (the author of Alice in Wonderland) was an amateur mathematician who wrote a book about determinants in 1866 and gave a copy to the queen. The queen dismissed the book and so did the math community for over a century. The Hodgson Condensation method resurfaced in the 80's as the fastest method to compute determinants (almost always, and almost surely). Interested about Lie groups, and their representations? In crystal bases? In cluster algebras? In alternating sign matrices? OK, how about square ice? Are you nuts? If so, come and listen.

Partitions of the Subset Lattice into Intervals

Series
Research Horizons Seminar
Time
Wednesday, September 16, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
William T. Trotter – School of Mathematics, Georgia Tech –

Please Note: (joint work with Csaba Biro, Dave Howard, Mitch Keller and Stephen Young. Biro and Young finished their Ph.D.'s at Georgia Tech in 2008. Howard and Keller will graduate in spring 2010)

Motivated by questions in algebra involving what is called "Stanley" depth, the following combinatorial question was posed to us by Herzog: Given a positive integer n, can you partition the family of all non-empty subsets of {1, 2, ..., n} into intervals, all of the form [A, B] where |B| is at least n/2. We answered this question in the affirmative by first embedding it in a stronger result and then finding two elegant proofs. In this talk, which will be entirely self-contained, I will give both proofs. The paper resulting from this research will appear in the Journal of Combinatorial Theory, Series A.

Some Problems and Results in Additive Combinatorics.

Series
Research Horizons Seminar
Time
Wednesday, September 9, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Ernie Croot – School of Mathematics, Georgia Tech –
Additive combinatorics is a relatively new field, with many diverse and exciting research programmes. In this talk I will discuss two of these programmes -- the continuing development of sum-product inequalities, and the unfolding progress on arithmetic progressions -- along with some new results proved by me and my collaborators. Hopefully I will have time to mention some nice research problems as well.

Did you hear what's going round?

Series
Research Horizons Seminar
Time
Wednesday, April 22, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Evans Harrell – School of Mathematics, Georgia Tech
The eigenvalues of the Laplacian are the squares of the frequencies of the normal modes of vibration, according to the wave equation. For this reason, Bers and Kac referred to the problem of determining the shape of a domain from the eigenvalue spectrum of the Laplacian as the question of whether one can "hear" the shape. It turns out that in general the answer is "no." Sometimes, however, one can, for instance in extremal cases where a domain, or a manifold, is round. There are many "isoperimetric" theorems that allow us to conclude that a domain, curve, or a manifold, is round, when enough information about the spectrum of the Laplacian or a similar operator is known. I'll describe a few of these theorems and show how to prove them by linking geometry with functional analysis.

Mathematical approaches to image processing

Series
Research Horizons Seminar
Time
Wednesday, April 15, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Sung Ha Kang – School of Mathematics, Georgia Tech
This talk will focus on mathematical approaches using PDE and variational models for image processing. I will discuss general problems arising from image reconstructions and segmentation, starting from Total Variation minimization (TV) model and Mumford-Shah segmentation model, and present new models from various developments. Two main topics will be on variational approaches to image reconstruction and multi-phase segmentation. Many challenges and various problems will be presented with some numerical results.

PDE Techniques in Wavelet Transforms and Applications Image Processing, Part II

Series
Research Horizons Seminar
Time
Wednesday, April 8, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Hao Min Zhou – School of Mathematics, Georgia Tech
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.

PDE Techniques in Wavelet Transforms and Applications Image Processing

Series
Research Horizons Seminar
Time
Wednesday, March 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Hao Min Zhou – School of Mathematics, Georgia Tech
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.

Quantum Statistical Mechanics, graphs and determinants

Series
Research Horizons Seminar
Time
Wednesday, February 25, 2009 - 12:00 for 2 hours
Location
Skiles 255
Speaker
Federico Bonetto – School of Mathematics, Georgia Tech
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.

Kirchhoff's matrix-tree theorem revisited

Series
Research Horizons Seminar
Time
Wednesday, February 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Matt Baker – School of Mathematics, Georgia Tech
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.

Intersections of Schubert varieties and eigenvalue inequalities

Series
Research Horizons Seminar
Time
Wednesday, February 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Wing Suet Li – School of Mathematics, Georgia Tech
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.

Pages