Seminars and Colloquia Schedule

The left frontal lobe´s role in language

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 20, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Christopher Rorden – Center for Advanced Brain Imaging (Gatech/GSU)
This talk showcases how we can use emerging methods to understand brainfunction. Many of the techniques described could be optimized usingtechniques being developed by researchers in the GT Mathematicsdepartment. A primary tenet of neuroscience is that the left frontal lobeis crucial for speech production and the posterior regions of the lefthemisphere play a critical role in language comprehension and wordretrieval. However, recent work shows suggests the left frontal lobe mayalso aid in tasks classically associated with posterior regions, such asvisual speech perception. We provide new evidence for this notion based onthe use brain imaging (structural and functional MRI) and brainstimulation techniques (TMS and tDCS) in both healthy individuals andpeople with chronic stroke. Our work takes these theoretical findings andtests them in a clinical setting. Specifically, our recent work suggeststhat stimulation of the frontal cortex may complement speech therapy inchronic stroke. Our recent brain stimulation work using transcranialdirect current stimulation supports this hypothesis, illustrating smallbut statistically significant benefits in anomia following brainstimulation.

An unusual duality principle for fully nonlinear equations

Series
PDE Seminar
Time
Tuesday, September 21, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Professor Scott Armstrong – University of Chicago
We discuss how to solve a Hamilton-Jacobi-Bellman equation ``at resonance." Our characterization is in terms of invariant measures and is analogous to the Fredholm alternative in the linear case.   

Non-archimedean amoebas and tropical geometry

Series
Tropical Geometry Seminar
Time
Wednesday, September 22, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Matt Baker – Georgia Tech
I will discuss the correspondence between non-archimedean amoebas and tropical varieties, which is a generalization of the theory of Newton polygons to polynomials in several variables.

Eigenvalues and the shapes of very small things

Series
Research Horizons Seminar
Time
Wednesday, September 22, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Evans Harell – School of Mathematics - Georgia Institute of Technology

Hosts: Yao Li and Ricardo Restrepo

When an object is small enough that quantum mechanics matters, many of its physical properties, such as energy levels, are determined by the eigenvalues of some linear operators. For quantum wires, waveguides, and graphs, geometry and topology show up in the operators and affect the set of eigenvalues, known as the spectrum. It turns out that the spectrum can't be just any sequence of numbers, both because of some general theorems about the eigenvalues and because of inequalities involving the shape. I'll discuss some of the extreme cases that test the theorems and inequalities and connect them to the shapes of the structures and to algebraic properties of the operators.To understand this lecture it would be helpful to know a little about PDEs and eigenvalues, but no knowledge of quantum mechanics will be needed.

A non-commutative Wiener Inversion Theorem and Schroedinger dispersive estimates

Series
Analysis Seminar
Time
Wednesday, September 22, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Michael Goldberg – University of Cincinnati –
We prove an extension of the Wiener inversion theorem for convolution of summable series, allowing the terms to take values in a space of bounded linear operators. The resulting algebra is no longer commutative due to the composition of operators. Inversion theorems arise naturally in the context of proving dispersive estimates for the Schr\"odinger and wave equation and lead to scale-invariant conditions for the class of admissible potentials. All results are joint work with Marius Beceanu.

Choosability of planar graphs

Series
Graph Theory Seminar
Time
Thursday, September 23, 2010 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Zdenek Dvorak – Charles University, Prague, Czech Republic
A graph is k-choosable if it can be properly colored from any assignment of lists of colors of length at least k to its vertices. A well-known results of Thomassen state that every planar graph is 5-choosable and every planar graph of girth 5 is 3-choosable. These results are tight, as shown by constructions of Voigt. We review some new results in this area, concerning 3-choosability of planar graphs with constraints on triangles and 4-cycles.

Small Noise: Dynamical Systems and Probability put together

Series
SIAM Student Seminar
Time
Friday, September 24, 2010 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Serjio Almanda – School of Mathematics, Georgia Tech
In this talk I will outline a topic that has been of interest due to its applicability in physics and engineering. The so called small noise model is a very technical subject that lies in the center of probability theory and usually study thorough a large deviations approach. I will explain this terminology and why is the correlation with dynamical systems so strong. Recent developments will be given at the end if time allows.

Introduction to (some versions of) Heegaard-Floer Homology

Series
Geometry Topology Working Seminar
Time
Friday, September 24, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Amey Kaloti – Ga Tech
This will be an introduction to the basic aspects of Heegaard-Floer homology and knot Heegaard-Floer homology. After this talk (talks) we will be organizing a working group to go through various computations and results in knot Heegaard-Floer theory and invariants of Legendrian knots.

Small-time statistical behavior of Levy processes and its application to the estimation and pricing of Levy-based financial models

Series
Mathematical Finance/Financial Engineering Seminar
Time
Friday, September 24, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
J.E. Figueroa-Lopez – Purdue University
The first order small-time approximation of the marginal distribution of a L\'evy process has been known for long-time. In this talk, I present higher order expansions polynomial in time for the distributions of a L\'evy process. As a secondary objective, I illustrate the application of our expansions in the estimation of financial models with jumps as well as in the study of the small-term asymptotic behavior of the implied volatility for this class of financial models. This talk presents joint work with C. Houdr\'e and M. Forde. Associated reading (available in the web site of the speaker): (1) Small-time expansions for the transition distribution of Levy processes. J.E. Figueroa-L\'opez and C. Houdré. Stochastic Processes and their Applications 119 pp. 3862-3889, 2009. (2) Nonparametric estimation of time-changed Levy models under high-frequency data. J.E. Figueroa-L\'opez. Advances in Applied Probability vol. 41, number 4, pp. 1161-1188, 2009. (3) The small-maturity smile for exponential Levy model. J.E. Figueroa-L\'opez and M. Forde. Preprint.

Crossings and nestings of two edges in set partitions

Series
Combinatorics Seminar
Time
Friday, September 24, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Svetlana Poznanovikj – SoM, Georgia Tech
A set partition of [n] can be represented graphically by drawing n dots on a horizontal line and connecting the points in a same block by arcs. Crossings and nestings are then pairs of arcs that cross or nest. Let G be an abelian group, and \alpha, \beta \in G. In this talk I will look at the distribution of the statistic s_{\alpha, \beta} = \alpha * cr + \beta * ne on subtrees of the tree of all set partitions and present a result which says that the distribution of s_{\alpha, \beta} on a subtree is determined by its distribution on the first two levels.