Seminars and Colloquia by Series

Algebraic theory for discrete models in systems biology

Series
Mathematical Biology Seminar
Time
Wednesday, September 21, 2011 - 23:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Franziska Hinkelmann – Mathematical Biosciences Institute, Ohio State University
Systems biology aims to explain how a biological system functions by investigating the interactions of its individual components from a systems perspective. Modeling is a vital tool as it helps to elucidate the underlying mechanisms of the system. My research is on methods for inference and analysis of polynomial dynamical systems (PDS). This is motivated by the fact that many discrete model types, e.g., Boolean networks or agent-based models, can be translated into the framework of PDS, that is, time- and state-discrete dynamical systems over a finite field where the transition function for each variable is given as a polynomial. This allows for using a range of theoretical and computational tools from computer algebra, which results in a powerful computational engine for model construction, parameter estimation, and analysis methods such as steady state behavior and optimal control. For model inference problems, the algebraic structure of PDS allows for efficient restriction of the model space to canalyzing functions, resulting in a subset of Boolean networks with "nice" biological properties.

Dynamic Modeling and Prediction of Risk Neutral Densities

Series
Mathematical Finance/Financial Engineering Seminar
Time
Wednesday, September 21, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Instr. Center 111
Speaker
Rong Chen – Department of Statistics, Rutgers University

Please Note: Hosted by Christian Houdre and Liang Peng

Risk neutral density is extensively used in option pricing and risk management in finance. It is often implied using observed option prices through a complex nonlinear relationship. In this study, we model the dynamic structure of risk neutral density through time, investigate modeling approach, estimation method and prediction performances. State space models, Kalman filter and sequential Monte Carlo methods are used. Simulation and real data examples are presented.

Sharp Trace Inequality for the Fractional Laplacian.

Series
Research Horizons Seminar
Time
Wednesday, September 21, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amit Einav – Georgia Tech
Sharp trace inequalities play a major role in the world of Mathematics. Not only do they give a connection between 'boundary values' of the trace and 'interior values' of the function, but also the truest form of it, many times with a complete classification of when equality is attained. The result presented here, motivated by such inequality proved by Jose' Escobar, is a new trace inequality, connecting between the fractional laplacian of a function and its restriction to the intersection of the hyperplanes x_(n)=0, x_(n-1)=0, ..., x_(n-j+1)=0 where 1<=j<=n. We will show that the inequality is sharp and discussed the natural space for it, along with the functions who attain equality in it. The above result is based on a joint work with Prof. Michael Loss.

The ABP maximum principle for fully nonlinear PDE with unbounded coefficients.

Series
PDE Seminar
Time
Tuesday, September 20, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Shigeaki Koike – Saitama University, Japan
In this talk, I will show recent results on the Aleksandrov-Bakelman-Pucci (ABP for short) maximum principle for $L^p$-viscosity solutions of fully nonlinear, uniformly elliptic partial differential equations with unbounded inhomogeneous terms and coefficients. I will also discuss some cases when the PDE has superlinear terms in the first derivatives. This is a series of joint works with Andrzej Swiech.

The Shafarevich-Tate group of an Elliptic Curve

Series
Algebra Seminar
Time
Monday, September 19, 2011 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Saikat Biswas – Georgia Tech
The rational solutions to the equation describing an elliptic curve form a finitely generated abelian group, also known as the Mordell-Weil group. Detemining the rank of this group is one of the great unsolved problems in mathematics. The Shafarevich-Tate group of an elliptic curve is an important invariant whose conjectural finiteness can often be used to determine the generators of the Mordell-Weil group. In this talk, we first introduce the definition of the Shafarevich-Tate group. We then discuss the theory of visibility, initiated by Mazur, by means of which non-trivial elements of the Shafarevich-Tate group of an elliptic curve an be 'visualized' as rational points on an ambient curve. Finally, we explain how this theory can be used to give theoretical evidence for the celebrated Birch and Swinnerton-Dyer Conjecture.

Construction of piecewise linear, continuous, orthogonal, wavelets on a regular hexagon

Series
Applied and Computational Mathematics Seminar
Time
Monday, September 19, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeff Geronimo – School of Mathematics, Georgia Tech
Using the technique of intertwining multiresolution analysis piecewise linear, continuous, orthogonal, wavelets on a regular hexagon are constructed. We will review the technique of intertwining multiresolution analysis in the one variable case then indicate the modifications necessary for the two variable construction. This is work with George Donovan and Doug Hardin.

On the slice-ribbon conjecture for Montesinos knots

Series
Geometry Topology Seminar
Time
Monday, September 19, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ana Garcia Lecuona – Penn State University
The slice-ribbon conjecture states that a knot in $S^3=partial D^4$ is the boundary of an embedded disc in $D^4$ if and only if it bounds a disc in $S^3$ which has only ribbon singularities. In this seminar we will prove the conjecture for a family of Montesinos knots. The proof is based on Donaldson's diagonalization theorem for definite four manifolds.

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, September 19, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Rohit Banga, Prashant Gaurav, and Manoj Soni – Georgia Tech
A discussion of the Chan & Ding (2008) paper "Boltzmann ensemble features of RNA secondary structures: a comparative analysis of biological RNA sequences and random shuffles."

Points covered by many simplices

Series
Graph Theory Seminar
Time
Friday, September 16, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Daniel Kral – Charles University, Prague, Czech Republic
Boros and Furedi (for d=2) and Barany (for arbitrary d) proved that there exists a constant c_d>0 such that for every set P of n points in R^d in general position, there exists a point of R^d contained in at least c_d n!/(d+1)!(n-d-1)! (d+1)-simplices with vertices at the points of P. Gromov [Geom. Funct. Anal. 20 (2010), 416-526] improved the lower bound on c_d by topological means. Using methods from extremal combinatorics, we improve one of the quantities appearing in Gromov's approach and thereby provide a new stronger lower bound on c_d for arbitrary d. In particular, we improve the lower bound on c_3 from 0.06332 due to Matousek and Wagner to more than 0.07509 (the known upper bound on c_3 is 0.09375). Joint work with Lukas Mach and Jean-Sebastien Sereni.

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