Seminars and Colloquia Schedule

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."

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.

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.

Motor-Cargo Dynamics in Microtubule-based Intracellular Transport

Series
Mathematical Biology Seminar
Time
Wednesday, October 5, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Scott McKinley – University of Florida
In this talk, we will consider a stochastic differential equation framework for analyzing the interaction between processive molecular motors, such as kinesin and dynein, and the biomolecular cargo they tow as part of microtubule-based intracellular transport. We show that the classical experimental environment is in a parameter regime which is qualitatively distinct from conditions one expects to find in living cells. However, an asymptotic analysis of the proposed system of SDEs permits one to take "in vitro" observations of the nonlinear response by motors to forces induced on the attached cargo, and make analytical predictions for two regimes that frustrate direct experimental observation: 1) highly viscous "in vivo" transport and 2) dynamics when multiple identical motors are attached to the cargo and microtubule.

Stein fillings on Lens spaces.

Series
Geometry Topology Student Seminar
Time
Wednesday, October 5, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amey Kaloti – Georgia Tech
In this talk we will outline proof due to Plameneveskaya and Van-Horn Morris that every virtually overtwisted contact structure on L(p,1) has a unique Stein filling. We will give a much simplified proof of this result. In addition, we will talk about classifying Stein fillings of ($L(p,q), \xi_{std})$ using only mapping class group basics.

SOLVING APPROXIMATELY SYSTEMS OF POLYNOMIAL EQUATIONS

Series
Algebra Seminar
Time
Wednesday, October 5, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Carlos Beltrán – University of Cantabria, Spain

[Note unusual day and time!]

In the last decades, path following methods have become a very popular strategy to solve systems of polynomial equations. Many of the advances are due to the correct understanding of the geometrical properties of an algebraic object, the so-called solution variety for polynomial system solving. I summarize here some of the most recent advances in the understanding of this object, focusing also on the certifcation and complexity of the numerical procedures involved in path following methods.

Testing Whether the Underlying Continuous-Time Process Follows a Diffusion: an Infinitesimal Operator Based Approach

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, October 5, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bin Chen – Department of Economics, University of Rochester

Hosted by Christian Houdre and Liang Peng

We develop a nonparametric test to check whether the underlying continuous time process is a diffusion, i.e., whether a process can be represented by a stochastic differential equation driven only by a Brownian motion. Our testing procedure utilizes the infinitesimal operator based martingale characterization of diffusion models, under which the null hypothesis is equivalent to a martingale difference property of the transformed processes. Then a generalized spectral derivative test is applied to check the martingale property, where the drift function is estimated via kernel regression and the diffusion function is integrated out by quadratic variation and covariation. Such a testing procedure is feasible and convenient because the infinitesimal operator of the diffusion process, unlike the transition density, has a closed-form expression of the drift and diffusion functions. The proposed test is applicable to both univariate and multivariate continuous time processes and has a N(0,1) limit distribution under the diffusion hypothesis. Simulation studies show that the proposed test has good size and all-around power against non-diffusion alternatives in finite samples. We apply the test to a number of financial time series and find some evidence against the diffusion hypothesis.

Some Properties of Random Networks

Series
Stochastics Seminar
Time
Thursday, October 6, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Haiyan Cai – Department of Mathematics and Computer Science, University of Missouri
I will talk briefly some of my recent research on random networks. In the first part of the talk, we will focus on the connectivity of a random network. The network is formed from a set of randomly located points and their connections depend on the distance between the points. It is clear that the probability of connection depends on the density of the points. We will explore some properties of this probability as a function of the point density. In the second part, I will discuss a possible approach in the study correlation structure of a large number of random variables. We will focus mainly on Gaussian distribution and distributions which are "similar" to Gaussian distributions. The idea is to use a single number to quantify the strength of correlation among all the random variables. Such a quantity can be derived from a latent cluster structure within a Markovian random network setting.

Holomorphic curves in geometry and topology V

Series
Geometry Topology Working Seminar
Time
Friday, October 7, 2011 - 14:00 for 2 hours
Location
Skiles 006
Speaker
John Etnyre – Ga Tech

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).