Seminars and Colloquia by Series

The analityicity transition in Frenkel-Kontorova models and XY models in 1-D

Series
Math Physics Seminar
Time
Tuesday, October 25, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rafael De la Llave – SoM Georgia Tech
We consider several models from solid state Physics and consider the problem offinding quasi-periodic solutions. We present a KAM theorem that showsthat given an approximate solution with good condition numbers, onecan find a true solution close by. The method of proof leads tovery efficient algorithms. Also it provides a criterion for breakdown.We will present the proof, the algorithms and some conjectures obtainedby computing in some cases. Much of the work was done with R. Calleja and X. Su.

From Sparsity to Rank, and Beyond: algebra, geometry, and convexity

Series
School of Mathematics Colloquium
Time
Monday, October 24, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pablo Parrilo – MIT –
Optimization problems involving sparse vectors or low-rank matrices are of great importance in applied mathematics and engineering. They provide a rich and fruitful interaction between algebraic-geometric concepts and convex optimization, with strong synergies with popular techniques like L1 and nuclear norm minimization. In this lecture we will provide a gentle introduction to this exciting research area, highlighting key algebraic-geometric ideas as well as a survey of recent developments, including extensions to very general families of parsimonious models such as sums of a few permutations matrices, low-rank tensors, orthogonal matrices, and atomic measures, as well as the corresponding structure-inducing norms.Based on joint work with Venkat Chandrasekaran, Maryam Fazel, Ben Recht, Sujay Sanghavi, and Alan Willsky.

Surface diagrams of smooth 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, October 24, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jonathan Williams – UGA
I will describe a new way to depict any smooth, closed oriented 4-manifold using a surface decorated with circles, along with a set of moves that relate any pair of such depictions.

A fast algorithm for finding the shortest path by solving initial value ODE's

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 24, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jun Lu – GT Math
We propose a new fast algorithm for finding the global shortest path connecting two points while avoiding obstacles in a region by solving an initial value problem of ordinary differential equations (ODE's). The idea is based on the factthat the global shortest path possesses a simple geometric structure. This enables us to restrict the search in a set of feasible paths that share the same structure. The resulting search space is reduced to a finite dimensional set. We use a gradient descent strategy based on the intermittent diffusion (ID) in conjunction with the level set framework to obtain the global shortest path by solving a randomly perturbed ODE's with initial conditions.Compared to the existing methods, such as the combinatorial methods or partial differential equation(PDE) methods, our algorithm is faster and easier to implement. We can also handle cases in which obstacles shape are arbitrary and/or the dimension of the base space is three or higher.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, October 24, 2011 - 11:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 114
Speaker
Todd Shayler – Georgia Tech
A discussion of the Allali and Sagot (2005) paper "A New Distance for High Level RNA Secondary Structure Comparison."

Triangulations and Resultants

Series
Combinatorics Seminar
Time
Friday, October 21, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josephine Yu – School of Math, Ga Tech
The secondary polytope of a point configuration A is a polytope whose faces are in bijection with regular subdivions of A, e.g. the secondary polytope of the vertices of polygon is an associahedron. The resultant of a tuple of point configurations A_1, A_2, ..., A_k in Z^n is the set of coefficients for which the polynomials with supports A_1, A_2, ..., A_k have a common root with no zero coordinates over complex numbers, e.g. when each A_1 is a standard simplex and k = n+1, the resultant is defined by a determinant. The Newton polytope of a polynomial is the convex hull of the exponents, e.g. the Newton polytope of the determinant is the perfect matching polytope. In this talk, I will explain the close connection between secondary polytopes and Newton polytopes of resultants, using tropical geometry, based on joint work with Anders Jensen.

Integrals of Characteristic Polynomials of Unitary Matrices, and Applications to the Riemann Zeta Function

Series
Stochastics Seminar
Time
Thursday, October 20, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Don Richards – Penn State, Department of Statistics
In work on the Riemann zeta function, it is of interest to evaluate certain integrals involving the characteristic polynomials of N x N unitary matrices and to derive asymptotic expansions of these integrals as N -> \infty. In this talk, I will obtain exact formulas for several of these integrals, and relate these results to conjectures about the distribution of the zeros of the Riemann zeta function on the critical line. I will also explain how these results are related to multivariate statistical analysis and to the hypergeometric functions of Hermitian matrix argument.

Some Remarkable Structured Investment Vehicles, and the Spectacular Financial Crisis of 2008-2018

Series
Mathematical Finance/Financial Engineering Seminar
Time
Thursday, October 20, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Don Richards – Penn State, Department of Statistics

Please Note: Hosted by Christian Houdre and Liang Peng

At this time, in late September, 2011 the Dow Jones Industrial Average has just suffered its worst week since October, 2008; the Standard & Poor 500 Average just completed its worst week in the past five years; and financial markets worldwide under severe stress. We think it is timely to look at aspects of the role played by "financial engineering" (also known as "mathematical finance" or "quantitative finance") in the genesis of the on-going crisis. In this talk, we examine several structured investment vehicles (SIVs) devised by financial engineers and sold worldwide to many "investors". It will be seen that these SIVs were doomed from inception. In light of these results, we are dismayed by the mathematical models propagated over the past decade by financial ``engineers'' and ``experts'' in structured finance, and it heightens our fears about the durability of the on-going worldwide financial crisis.

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