Seminars and Colloquia by Series

Construction of piecewise linear, continuous, orthogonal, wavelets on a regular hexagon

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 19, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeff Geronimo – School of Mathematics, Georgia Tech
Using the technique of intertwining multiresolution analysis piecewise linear, continuous, orthogonal, wavelets on a regular hexagon are constructed. We will review the technique of intertwining multiresolution analysis in the one variable case then indicate the modifications necessary for the two variable construction. This is work with George Donovan and Doug Hardin.

On the slice-ribbon conjecture for Montesinos knots

Series
Geometry Topology Seminar
Time
Monday, September 19, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ana Garcia Lecuona – Penn State University
The slice-ribbon conjecture states that a knot in $S^3=partial D^4$ is the boundary of an embedded disc in $D^4$ if and only if it bounds a disc in $S^3$ which has only ribbon singularities. In this seminar we will prove the conjecture for a family of Montesinos knots. The proof is based on Donaldson's diagonalization theorem for definite four manifolds.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, September 19, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Rohit Banga, Prashant Gaurav, and Manoj Soni – Georgia Tech
A discussion of the Chan & Ding (2008) paper "Boltzmann ensemble features of RNA secondary structures: a comparative analysis of biological RNA sequences and random shuffles."

Points covered by many simplices

Series
Graph Theory Seminar
Time
Friday, September 16, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Kral – Charles University, Prague, Czech Republic
Boros and Furedi (for d=2) and Barany (for arbitrary d) proved that there exists a constant c_d>0 such that for every set P of n points in R^d in general position, there exists a point of R^d contained in at least c_d n!/(d+1)!(n-d-1)! (d+1)-simplices with vertices at the points of P. Gromov [Geom. Funct. Anal. 20 (2010), 416-526] improved the lower bound on c_d by topological means. Using methods from extremal combinatorics, we improve one of the quantities appearing in Gromov's approach and thereby provide a new stronger lower bound on c_d for arbitrary d. In particular, we improve the lower bound on c_3 from 0.06332 due to Matousek and Wagner to more than 0.07509 (the known upper bound on c_3 is 0.09375). Joint work with Lukas Mach and Jean-Sebastien Sereni.

Holomorphic curves in geometry and topology III

Series
Geometry Topology Working Seminar
Time
Friday, September 16, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Recall this is a 2 hour seminar (2-4).

This series of talks will be an introduction to the use of holomorphic curves in geometry and topology. I will begin by stating several spectacular results due to Gromov, McDuff, Eliashberg and others, and then discussing why, from a topological perspective, holomorphic curves are important. I will then proceed to sketch the proofs of the previously stated theorems. If there is interest I will continue with some of the analytic and gometric details of the proof and/or discuss Floer homology (ultimately leading to Heegaard-Floer theory and contact homology).

Potts models on Erdos-Renyi random graphs

Series
Stochastics Seminar
Time
Thursday, September 15, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shannon L. Starr – University of Rochester –
The Potts antiferromagnet on a random graph is a model problem from disordered systems, statistical mechanics with random Hamiltonians. Bayati, Gamarnik and Tetali showed that the free energy exists in the thermodynamic limit, and demonstrated the applicability of an interpolation method similar to one used by Guerra and Toninelli, and Franz and Leone for spin glasses. With Contucci, Dommers and Giardina, we applied interpolation to find one-sided bounds for the free energy using the physicists' ``replica symmetric ansatz.'' We also showed that for sufficiently high temperatures, this ansatz is correct. I will describe these results and some open questions which may also be susceptible to the interpolation method.

On the coefficients of a bivariate rational function

Series
School of Mathematics Colloquium
Time
Thursday, September 15, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robin Pemantle – Math, University of Pennsylvania –
Problem: describe the asymptotic behavior of the coefficients a_{ij} of the Taylor series for 1/Q(x,y) where Q is a polynomial. This problem is the simplest of a number of such problems arising in analytic combinatorics whose answer was not until recently known. In joint work with J. van der Hoeven and T. DeVries, we give a solution that is completely effective and requires only assumptions that are met in the generic case. Symbolic algebraic computation and homotopy continuation tools are required for implementation.

An introduction to Aubry-Mather theory

Series
Research Horizons Seminar
Time
Wednesday, September 14, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005.
Speaker
Rafael De La Llave – Georgia Tech.
Starting in the 30's Physicists were concerned with the problem of motion of dislocations or the problem of deposition of materials over a periodic structure. This leads naturally to a variational problem (minimizing the energy). One wants to know very delicate properties of the minimizers, which was a problem that Morse was studying at the same time. The systematic mathematical study of these problems started in the 80's with the work of Aubry and Mather who developed the basis to deal with very subtle problems. The mathematics that have become useful include dynamical systems, partial differential equations, calculus of variations and numerical analysis. Physical intuition also helps. I plan to explain some of the basic questions and, perhaps illustrate some of the results.

Dynamics in eigendirections of pseudo-Anosov maps on certain doubly periodic flat surfaces

Series
Geometry Topology Seminar
Time
Monday, September 12, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin Schmoll – Clemson U
We consider particle dynamics in the (unfolded) Ehrenfest Windtree Model and theflow along straight lines on a certain folded complex plane. Fixing some parameters,it turns out that both doubly periodic models cover one and the same L-shaped surface.We look at the case for which that L-shaped surface has a (certain kind of) structure preservingpseudo-Anosov. The dynamics in the eigendirection(s) of the pseudo-Anosovon both periodic covers is very different:The orbit diverges on the Ehrenfest model, but is dense on the folded complex plane.We show relations between the two models and present constructions of folded complex planes.If there is time we sketch some of the arguments needed to show escaping & density of orbits.There will be some figures showing the trajectories in different settings.

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