Seminars and Colloquia by Series

Ground state for nonlinear Schrodinger equation with sign-changing and vanishing potential.

Series
PDE Seminar
Time
Tuesday, October 4, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Zhengping Wang – Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, and Georgia Tech
We consider the stationary nonlinear Schrodinger equation when the potential changes sign and may vanish at infinity. We prove that there exists a sign-changing ground state and the so called energy doubling property for sign-changing solutions does not hold. Furthermore, we find that the ground state energy is not equal to the infimum of energy functional over the Nehari manifold. These phenomena are quite different from the case of positive potential.

High Accuracy Eigenvalue Approximation by the Finite Element Method

Series
Applied and Computational Mathematics Seminar
Time
Monday, October 3, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhimin Zhang – Wayne State University
Finite element approximations for the eigenvalue problem of the Laplace  operator are discussed. A gradient recovery scheme is proposed to enhance  the finite element solutions of the eigenvalues. By reconstructing the  numerical solution and its gradient, it is possible to produce more accurate  numerical eigenvalues. Furthermore, the recovered gradient can be used to  form an a posteriori error estimator to guide an adaptive mesh refinement.  Therefore, this method works not only for structured meshes, but also for  unstructured and adaptive meshes. Additional computational cost for this  post-processing technique is only O(N) (N is the total degrees of freedom),   comparing with O(N^2) cost for the original problem.

Morse 2-functions on 4-manifolds

Series
Geometry Topology Seminar
Time
Monday, October 3, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David Gay – UGA
Rob Kirby and I have been thinking for a while now about stable maps to 2-manifolds, which we call "Morse 2-functions", to stress the analogy with standard Morse theory, which studies stable maps to 1-manifolds. In this talk I will focus on the extent to which we can extend that analogy to the way in which handle decompositions combinatorialize Morse functions, especially in low dimensions. By drawing the images of attaching maps and some extra data, one describes the total space of a Morse function and the Morse function, up to diffeomorphism. I will discuss how much of that works in the context of Morse 2-functions. This is important because Rob Kirby and I have spent most of our time thinking about stable homotopies between Morse 2-functions, which should be thought of as giving "moves" between Morse 2-functions, but to honestly call them "moves" we need to make sure we have a reasonable way to combinatorialize Morse 2-functions to begin with.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, October 3, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Emily Rogers – Georgia Tech
A discussion of the Ding, Chan, and Lawrence paper (2005) "RNA secondary structure prediction by centroids in a Boltzmann weighted ensemble."

Polynomial Patterns in Subsets of the Integers

Series
Combinatorics Seminar
Time
Friday, September 30, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alex Rice – University of Georgia
How large can a subset of the first N natural numbers be before it is guaranteed to contain two distinct elements which differ by a perfect square? What if I replaced "perfect square" with the image of a more general polynomial, or perhaps "one less than a prime number"? We will discuss results of this flavor, including recent improvements and generalizations.

Holomorphic curves in geometry and topology IV

Series
Geometry Topology Working Seminar
Time
Friday, September 30, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

Please Note: Recall this is a 2 hour seminar.

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).

Steady-state $GI/GI/n$ queue in the Halfin-Whitt Regime

Series
Stochastics Seminar
Time
Thursday, September 29, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Goldberg – ISyE, Georgia Tech
In this talk, we resolve several questions related to a certain heavy traffic scaling regime (Halfin-Whitt) for parallel server queues, a family of stochastic models which arise in the analysis of service systems. In particular, we show that the steady-state queue length scales like $O(\sqrt{n})$, and bound the large deviations behavior of the limiting steady-state queue length. We prove that our bounds are tight for the case of Poisson arrivals. We also derive the first non-trivial bounds for the steady-state probability that an arriving customer has to wait for service under this scaling. Our bounds are of a structural nature, hold for all $n$ and all times $t \geq 0$, and have intuitive closed-form representations as the suprema of certain natural processes. Our upper and lower bounds also exhibit a certain duality relationship, and exemplify a general methodology which may be useful for analyzing a variety of stochastic models. The first part of the talk is joint work with David Gamarnik.

On the Square Dependence Problem

Series
School of Mathematics Colloquium
Time
Thursday, September 29, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ernie Croot – Georgia Tech
In many integer factoring algorithms, one produces a sequence of integers (created in a pseudo-random way), and wishes to rapidly determine a subsequence whose product is a square (which we call a `square product'). In his lecture at the 1994 International Congress of Mathematicians, Pomerance observed that the following problem encapsulates all of the key issues: Select integers a1, a2, ..., at random from the interval [1,x], until some (non-empty) subsequence has product equal to a square. Find good esimates for the expected stopping time of this process. A good solution to this problem should help one to determine the optimal choice of parameters for one's factoring algorithm, and therefore this is a central question. In this talk I will discuss the history of this problem, and its somewhat recent solution due to myself, Andrew Granville, Robin Pemantle, and Prasad Tetali.

New Exciting Approaches to Particle Scattering Amplitudes

Series
Math Physics Seminar
Time
Wednesday, September 28, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Marcus Nanotech Conference
Speaker
Henriette Elvang – Physics Department, University of Michigan

Please Note: Hosted by Predrag Cvitanovic, School of Physics

Particle scattering processes at experiments such as the Large Hadron Collider at CERN are described by scattering amplitudes. In quantum field theory classes, students learn to calculate amplitudes using Feynman diagram methods. This is a wonderful method for a process like electron + positron -> muon^- + muon^+, but it is a highly challenging for a process like gluon+gluon -> 5 gluons, which requires 149 diagrams even at the leading order in perturbation theory. It turns out, however, that the result for such gluon scattering processes is remarkably simple, in some cases it is just a single term! This has lead to new methods for calculating scattering amplitudes, and it has revealed that amplitudes have a surprisingly rich mathematical structure. The applications of these new methods range from calculation of processes relevant for LHC physics to theoretical explorations of quantum gravity. I will give a pedagogical introduction to these new approaches to scattering theory and their applications, not assuming any prior knowledge of quantum field theory or Feynman rules.

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