Seminars and Colloquia by Series

Scaling limits for the exit problem for conditioned diffusions via Hamilton-Jacobi equations

Series
Stochastics Seminar
Time
Thursday, September 12, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yuri Bakhtin – GaTech
The classical Freidlin--Wentzell theory on small random perturbations of dynamical systems operates mainly at the level of large deviation estimates. In many cases it would be interesting and useful to supplement those with central limit theorem type results. We are able to describe a class of situations where a Gaussian scaling limit for the exit point of conditioned diffusions holds. Our main tools are Doob's h-transform and new gradient estimates for Hamilton--Jacobi equations. Joint work with Andrzej Swiech.

Potential Theory in the Complex Plane and Polynomials

Series
Research Horizons Seminar
Time
Wednesday, September 11, 2013 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Doron Lubinsky – School of Mathematics
We'll look at some of the basics of potential theory in the complex plane. We'll also discuss how potential theory may be used in studying zeros of polynomials and approximation theory.

Towards the directed cycle double cover conjecture

Series
Graph Theory Seminar
Time
Tuesday, September 10, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Martin Loebl – Charles University
We prove the dcdc conjecture in a class of lean fork graphs, argue that this class is substantial and show a path towards the complete solution. Joint work with Andrea Jimenez.

Teaching opportunities at Tech

Series
Professional Development Seminar
Time
Tuesday, September 10, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christine Heitsch – Georgia Tech
A panel discussion with Luz Vela-Arevalo, Klara Grodzinsky, Chris Heil, and Dia Sekayi, CETL's Assistant Director for Education.

Noetherianity for infinite-dimensional toric ideals

Series
Algebra Seminar
Time
Monday, September 9, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Krone – Georgia Tech –
Given a family of ideals which are symmetric under some group action on the variables, a natural question to ask is whether the generating set stabilizes up to symmetry as the number of variables tends to infinity. We answer this in the affirmative for a broad class of toric ideals, settling several open questions in work by Aschenbrenner-Hillar, Hillar-Sullivant, and Hillar-Martin del Campo. The proof is largely combinatorial, making use of matchings on bipartite graphs, and well-partial orders.

Complete nonnegatively curved planes

Series
Geometry Topology Seminar
Time
Monday, September 9, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Igor Belegradek – Georgia Tech
It is known that any complete nonnegatively curved metric on the plane is conformally equivalent to the Euclidean metric. In the first half of the talk I shall explain that the conformal factors that show up correspond precisely to smooth subharmonic functions of minimal growth. The proof is function-theoretic. This characterization of conformal factors can be used to study connectedness properties of the space of complete nonnegatively curved metrics on the plane. A typical result is that the space of metrics cannot be separated by a finite dimensional subspace. The proofs use infinite-dimensional topology and dimension theory. This is a joint work with Jing Hu.

Numerical methods for highly oscillatory dynamical systems using multiscale structure

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 9, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Seong Jun Kim – GT Math
The main aim of this talk is to design efficient and novel numerical algorithms for highly oscillatory dynamical systems with multiple time scales. Classical numerical methods for such problems need temporal resolution to resolve the finest scale and become very inefficient when the longer time intervals are of interest. In order to accelerate computations and improve the long time accuracy of numerical schemes, we take advantage of various multiscale structures established from a separation of time scales. The framework of the heterogeneous multiscale method (HMM) will be considered as a general strategy both for the design and for the analysis of multiscale methods.(Keywords: Multiscale oscillatory dynamical systems, numerical averaging methods.)

James periodicity and the EHP sequence I

Series
Geometry Topology Working Seminar
Time
Friday, September 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kirsten Wickelgren – Georgia Tech

Please Note: Note this is a 1 hour seminar (not the usual 2 hours).

Allowing formal desuspensions of maps and objects takes the category of topological spaces to the category of spectra, where cohomology is naturally represented. The EHP spectral sequence encodes how far one can desuspend maps between spheres. It's among the most useful tools for computing homotopy groups of spheres. RP^infty has a cell structure with a cell in each dimension and with attaching maps of degrees ...020202... Note that this sequence is periodic. In fact, it is more than the degrees of these maps which are periodic and a map of Snaith relates this periodicity to the EHP sequence.We will develop the EHP sequence, James periodicity and the relationship between the two.

Shy and fixed distance couplings on Riemanian manifolds

Series
Stochastics Seminar
Time
Thursday, September 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
006
Speaker
Ionel Popescu – GaTech
We show that on any Riemannian manifold with the Ricci curvature non-negative we can construct a coupling of two Brownian motions which are staying fixed distance for all times. We show a more general version of this for the case of Ricci bounded from below uniformly by a constant k. In the terminology of Burdzy, Kendall and others, a shy coupling is a coupling in which the Brownian motions do not couple in finite time with positive probability. What we construct here is a strong version of shy couplings on Riemannian manifolds. On the other hand, this can be put in contrast with some results of von Renesse and K. T. Sturm which give a characterization of the lower bound on the Ricci curvature in terms of couplings of Brownian motions and our construction optimizes this choice in a way which will be explained. This is joint work with Mihai N. Pascu.

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