Seminars and Colloquia Schedule

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, January 23, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Shel Swenson – Georgia Tech
A discussion of the paper "Beyond energy minimization: approaches to the kinetic folding of RNA'' by Flamm and Hofacker (2008).

A numerical algorithm for the computation of periodic orbits of the Kuramoto-Sivashinsky equation.

Series
CDSNS Colloquium
Time
Monday, January 23, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jordi Lluis Figueras – Uppsala University
In this talk we will present a numerical algorithm for the computation of (hyperbolic) periodic orbits of the 1-D K-S equation u_t+v*u_xxxx+u_xx+u*u_x = 0, with v>0. This numerical algorithm consists on apply a suitable Newton scheme for a given approximate solution. In order to do this, we need to rewrite the invariance equation that must satisfy a periodic orbit in a form that its linearization around an approximate solution is a bounded operator. We will show also how this methodology can be used to compute rigorous estimates of the errors of the solutions computed.

Parallel heat transport in reverse shear magnetic fields

Series
Math Physics Seminar
Time
Monday, January 23, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel Blazevski – University of Texas
I will discuss local and nonlocal anisotropic heat transport along magnetic field lines in a tokamak, a device used to confine plasma undergoing fusion. I will give computational results that relate certain dynamical features of the magnetic field, e.g. resonance islands, chaotic regions, transport barriers, etc. to the asymptotic temperature profiles for heat transport along the magnetic field lines.

The cohomology groups of the pure string motion group are uniformly representation stable

Series
Geometry Topology Seminar
Time
Monday, January 23, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jenny Wilson – University of Chicago
In the past two years, Church, Farb and others have developed the concept of 'representation stability', an analogue of homological stability for a sequence of groups or spaces admitting group actions. In this talk, I will give an overview of this new theory, using the pure string motion group P\Sigma_n as a motivating example. The pure string motion group, which is closely related to the pure braid group, is not cohomologically stable in the classical sense -- for each k>0, the dimension of the H^k(P\Sigma_n, \Q) tends to infinity as n grows. The groups H^k(P\Sigma_n, \Q) are, however, representation stable with respect to a natural action of the hyperoctahedral group W_n, that is, in some precise sense, the description of the decomposition of the cohomology group into irreducible W_n-representations stabilizes for n>>k. I will outline a proof of this result, verifying a conjecture by Church and Farb.

Linear and nonlinear vibration-based energy harvesting

Series
Applied and Computational Mathematics Seminar
Time
Monday, January 23, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alper Erturk – Georgia Tech, School of Mechanical Engineering
The transformation of vibrations into low-power electricity has received growing attention over the last decade. The goal in this research field is to enable self-powered electronic components by harvesting the vibrational energy available in their environment. This talk will be focused on linear and nonlinear vibration-based energy harvesting using piezoelectric materials, including the modeling and experimental validation efforts. Electromechanical modeling discussions will involve both distributed-parameter and lumped-parameter approaches for quantitative prediction and qualitative representation. An important issue in energy harvesters employing linear resonance is that the best performance of the device is limited to a narrow bandwidth around the fundamental resonance frequency. If the excitation frequency slightly deviates from the resonance condition, the power output is drastically reduced. Energy harvesters based on nonlinear configurations (e.g., monostable and bistable Duffing oscillators with electromechanical coupling) offer rich nonlinear dynamic phenomena and outperform resonant energy harvesters under harmonic excitation over a range of frequencies. High-energy limit-cycle oscillations and chaotic vibrations in strongly nonlinear bistable beam and plate configurations are of particular interest. Inherent material nonlinearities and dissipative nonlinearities will also be discussed. Broadband random excitation of energy harvesters will be summarized with an emphasis on stochastic resonance in bistable configurations. Recent efforts on aeroelastic energy harvesting as well as underwater thrust and electricity generation using fiber-based flexible piezoelectric composites will be addressed briefly.

Using Mass formulas to Enumerate Definite Quadratic Forms of Bounded Class Number

Series
Algebra Seminar
Time
Tuesday, January 24, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jonathan Hanke – University of Georgia
This talk will describe some recent results using exact massformulas to determine all definite quadratic forms of small class number inn>=3 variables, particularly those of class number one.The mass of a quadratic form connects the class number (i.e. number ofclasses in the genus) of a quadratic form with the volume of its adelicstabilizer, and is explicitly computable in terms of special values of zetafunctions. Comparing this with known results about the sizes ofautomorphism groups, one can make precise statements about the growth ofthe class number, and in principle determine those quadratic forms of smallclass number.We will describe some known results about masses and class numbers (overnumber fields), then present some new computational work over the rationalnumbers, and perhaps over some totally real number fields.

Chemical reaction systems with toric steady states

Series
Mathematical Biology Seminar
Time
Wednesday, January 25, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anne Shiu – University of Chicago
Chemical reaction networks taken with mass-action kinetics are dynamical systems governed by polynomial differential equations that arise in systems biology. In general, establishing the existence of (multiple) steady states is challenging, as it requires the solution of a large system of polynomials with unknown coefficients. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. This talk focuses on systems with this property, are we say such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to admit toric steady states. Furthermore, we analyze the capacity of such a system to exhibit multiple steady states. An important application concerns the biochemical reaction networks networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism. No prior knowledge of chemical reaction network theory or binomial ideals will be assumed. (This is joint work with Carsten Conradi, Mercedes P\'erez Mill\'an, and Alicia Dickenstein.)

A Survey of Some Results Related to Roth's Theorem

Series
Research Horizons Seminar
Time
Wednesday, January 25, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ernie Croot – School of Mathematics, Georgia Tech
In this talk I will survey some recent results related to Roth's Theorem on three-term arithmetic progressions. The basic problem in this area is to determine the largest subset S of the integers in {1,...,n} containing no triple of the form x, x+d, x+2d. Roth showed back in the 1950's that the largest such set S has size o(n), and over the following decades his result has been considerably improved upon.

Characteristic Classes

Series
Geometry Topology Student Seminar
Time
Wednesday, January 25, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bulent Tosun – Georgia Tech
The aim of the talk is to give a complete proof of the fact that any closed oriented 3-manifold has a trivial tangent bundle.

Two weight inequality for the Hilbert transform

Series
Analysis Seminar
Time
Wednesday, January 25, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael Lacey – Georgia Tech
The two weight inequality for the Hilbert transform arises in the settings of analytic function spaces, operator theory, and spectral theory, and what would be most useful is a characterization in the simplest real-variable terms. We show that the $L^2$ to $L^2$ inequality holds if and only if two $L^2$ to weak-$L^2$ inequalities hold. This is a corollary to a characterization in terms of a two-weight Poisson inequality, and a pair of testing inequalities on bounded functions. Joint work with Eric Sawyer, Chun-Yun Shen, and Ignacio Uriate-Tuero.

Modeling Insurance in the Presence of Dependent Extreme Risks

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, January 25, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Qihe Tang – Department of Statistics and Actuarial Science, University of Iowa

Hosts: Christian Houdre and Liang Peng.

The prevalence of rare events accompanied by disastrous economic and social consequences, the so-called Black-Swan events, makes today's world far different from just decades ago. In this talk, I shall address the issue of modeling the wealth process of an insurer in a stochastic economic environment with dependent insurance and financial risks. The asymptotic behavior of the finite-time ruin probability will be studied. As an application, I shall discuss a portfolio optimization problem. This talk is based on recent joint works with Raluca Vernic and Zhongyi Yuan.

(Joint Combinatorics and Geometry Topology seminar) Combinatorics of Surface Deformations

Series
Additional Talks and Lectures
Time
Thursday, January 26, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Satyan Devadoss – Williams college –
We consider the moduli space of surfaces with boundary and marked points. Such spaces appear in algebraic geometry and topology, playing a strong role in holomorphic curves and open-closed string theory. We consider a combinatorial framework to view the compactification of this space based on the pair-of-pants decomposition of the surface, relating it to the well-known phenomenon of bubbling. This leads to a classification of all such spaces that can be realized as polytopes, capturing elegant hidden algebraic structure from homotopy theory. This talk is accessible to strong undergraduates, based heavily on pictures and concrete examples.

L-Moments: Inference for Distributions and Data Using Linear Combinations of Order Statistics

Series
Stochastics Seminar
Time
Thursday, January 26, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jon Hosking – IBM Research Division, T. J. Watson Research Center
L-moments are expectations of certain linear combinations of order statistics. They form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. L-moments are in analogous to the conventional moments, but are more robust to outliers in the data and enable more secure inferences to be made from small samples about an underlying probability distribution. They can be used for estimation of parametric distributions, and can sometimes yield more efficient parameter estimates than the maximum-likelihood estimates. This talk gives a general summary of L-moment theory and methods, describes some applications ranging from environmental data analysis to financial risk management, and indicates some recent developments on nonparametric quantile estimation, "trimmed" L-moments for very heavy-tailed distributions, and L-moments for multivariate distributions.

On the Maximum Number of Rich Lines in General Position

Series
Combinatorics Seminar
Time
Friday, January 27, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Chris Pryby and Albert Bush – School of Mathematics, Georgia Tech
A famous theorem of Szemeredi and Trotter established a bound on the maximum number of lines going through k points in the plane. J. Solymosi conjectured that if one requires the lines to be in general position -- no two parallel, no three meet at a point -- then one can get a much tighter bound. Using methods of G. Elekes, we establish Solymosi's conjecture on the maximum size of a set of rich lines in general position.