Seminars and Colloquia by Series

Dynamics of Functions with an Eventual Negative Schwarzian Derivative

Series
SIAM Student Seminar
Time
Friday, September 25, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Benjamin WebbSchool of Mathematics, Georgia Tech
In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this talk we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. The introduction of this class was motivated by some maps arising in neuroscience

The dynamics of moving interfaces in a random environment

Series
Stochastics Seminar
Time
Thursday, September 24, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jim NolenDuke University
I will describe recent work on the behavior of solutions to reaction diffusion equations (PDEs) when the coefficients in the equation are random. The solutions behave like traveling waves moving in a randomly varying environment. I will explain how one can obtain limit theorems (Law of Large Numbers and CLT) for the motion of the interface. The talk will be accessible to people without much knowledge of PDE.

The Asymmetric Simple Exclusion Process: Integrable Structure and Limit Theorems

Series
School of Mathematics Colloquium
Time
Thursday, September 24, 2009 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Distinguished Professor Craig TracyUniversity of California, Davis
The asymmetric simple exclusion process (ASEP) is a continuous time Markov process of interacting particles on a lattice \Gamma. ASEP is defined by two rules: (1) A particle at x \in \Gamma waits an exponential time with parameter one, and then chooses y \in \Gamma with probability p(x, y); (2) If y is vacant at that time it moves to y, while if y is occupied it remains at x. The main interest lies in infinite particle systems. In this lecture we consider the ASEP on the integer lattice {\mathbb Z} with nearest neighbor jump rule: p(x, x+1) = p, p(x, x-1) = 1-p and p \ne 1/2. The integrable structure is that of Bethe Ansatz. We discuss various limit theorems which in certain cases establishes KPZ universality.

Convergent Interpolation to Cauchy Integrals of Jacobi-type Weights and RH∂-Problems

Series
Analysis Seminar
Time
Wednesday, September 23, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Maxym YattselevVanderbilt University
We consider multipoint Padé approximation to Cauchy transforms of complex measures. First, we recap that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-continuous non-vanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. Second, we show that this convergence holds also for measures whose Radon–Nikodym derivative is a Jacobi weight modified by a Hölder continuous function. The asymptotics behavior of Padé approximants is deduced from the analysis of underlying non–Hermitian orthogonal polynomials, for which the Riemann–Hilbert–∂ method is used.

Locally ringed spaces

Series
Other Talks
Time
Wednesday, September 23, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Matt BakerSchool of Mathematics, Georgia Tech
I will discuss how various geometric categories (e.g. smooth manifolds, complex manifolds) can be be described in terms of locally ringed spaces. (A locally ringed space is a topological spaces endowed with a sheaf of rings whose stalks are local rings.) As an application of the notion of locally ringed space, I'll define what a scheme is.

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 GaroufalidisGeorgia 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.

Comparison principle for unbounded viscosity solutions of elliptic PDEs with superlinear terms in $Du$

Series
PDE Seminar
Time
Tuesday, September 22, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Shigeaki KoikeSaitama University, Japan
We discuss comparison principle for viscosity solutions of fully nonlinear elliptic PDEs in $\R^n$ which may have superlinear growth in $Du$ with variable coefficients. As an example, we keep the following PDE in mind:$$-\tr (A(x)D^2u)+\langle B(x)Du,Du\rangle +\l u=f(x)\quad \mbox{in }\R^n,$$where $A:\R^n\to S^n$ is nonnegative, $B:\R^n\to S^n$ positive, and $\l >0$. Here $S^n$ is the set of $n\ti n$ symmetric matrices. The comparison principle for viscosity solutions has been one of main issues in viscosity solution theory. However, we notice that we do not know if the comparison principle holds unless $B$ is a constant matrix. Moreover, it is not clear which kind of assumptions for viscosity solutions at $\infty$ is suitable. There seem two choices: (1) one sided boundedness ($i.e.$ bounded from below), (2) growth condition.In this talk, assuming (2), we obtain the comparison principle for viscosity solutions. This is a work in progress jointly with O. Ley.

Pricing Options on Assets with Jump Diffusion and Uncertain Volatility

Series
Mathematical Finance/Financial Engineering Seminar
Time
Tuesday, September 22, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Gunter MeyerSchool of Mathematics, Georgia Tech
When the asset price follows geometric Brownian motion but allows random Poisson jumps (called jump diffusion) then the standard Black Scholes partial differential for the option price becomes a partial-integro differential equation (PIDE). If, in addition, the volatility of the diffusion is assumed to lie between given upper and lower bounds but otherwise not known then sharp upper and lower bounds on the option price can be found from the Black Scholes Barenblatt equation associated with the jump diffusion PIDE. In this talk I will introduce the model equations and then discuss the computational issues which arise when the Black Scholes Barenblatt PIDE for jump diffusion is to be solved numerically.

Linear convergence of modified Frank-Wolfe algorithms for ellipsoid optimization algorithms

Series
Other Talks
Time
Tuesday, September 22, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
ISyE Executive Classroom, Main Building
Speaker
Michael J. ToddSchool of Operations Research and Information Engineering, Cornell University
We discuss the convergence properties of first-order methods for two problems that arise in computational geometry and statistics: the minimum-volume enclosing ellipsoid problem and the minimum-area enclosing ellipsoidal cylinder problem for a set of m points in R^n. The algorithms are old but the analysis is new, and the methods are remarkably effective at solving large-scale problems to high accuracy.

The uniform thickness property and iterated torus knots

Series
Geometry Topology Seminar
Time
Monday, September 21, 2009 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Doug LaFountainSUNY - Buffalo
The uniform thickness property (UTP) is a property of knots embeddedin the 3-sphere with the standard contact structure. The UTP was introduced byEtnyre and Honda, and has been useful in studying the Legendrian and transversalclassification of cabled knot types. We show that every iterated torus knotwhich contains at least one negative iteration in its cabling sequence satisfiesthe UTP. We also conjecture a complete UTP classification for iterated torusknots, and fibered knots in general.

Pages