Iowa State University Mathematics Colloquium
Fall 2005

Schedule of Talks

 

Date

Speaker

Title (Click on the title of a talk for the abstract if available).

Aug. 30,Tuesday

Yangbo Yang

University of Iowa

Prime number theorem for automorphic L-functions

 

Sep. 6, Tuesday

Yalcin Sarol

Iowa State University

Portfolio optimization in a Black-Scholes market driven by fractional Brownian motion

Sep. 13, Tuesday

Raffaele Romano

Iowa State University

The role of complete positivity in open quantum system dynamics

 

Sep. 20, Tuesday

Krishna Rajan

Iowa State University

Materials  Informatics: A new interface between the mathematical and materials sciences

 

Sep. 27, Tuesday

Jozsef Balogh

University of Illinois at Urbana-Champaign

Threshold growth cellular automata: bootstrap percolation

Oct. 4, Tuesday

Fred Goodman

University of Iowa

Tangles and algebras

 

Oct. 6, Thursday

William Sudderth

University of Minnesota

How to bid for a Pizza: An Introduction to  Stochastic Games

(Joint colloquium with dept. of Stat.)

Oct. 11, Tuesday

Amy Cohen

Rutgers University

How far can one push the inverse scattering method?

 

Oct. 18, Tuesday

Jerome W. Hoffman

Louisiana State University  

Zeta functions of graphs

Oct. 20, Thursday

Bhaba K. Sarma

Indian Institute of Technology Guwahati

 On corona of two graphs

Oct. 25, Tuesday

Paul Rabinowitz
University of Wisconsin

(Miller Lecture 305 Carver Hall)

Multi-transition solutions for a class of PDEs.

 

Nov. 3, Thursday

Chi-Wang Shu

Brown University

(This talk was canceled.)

Local Discontinuous Galerkin Methods for Dispersive Wave Equations 

 

Nov. 8, Tuesday

Leslie Hogben

Iowa State University

Combinatorial Matrix Theory

 

Nov. 15, Tuesday

Hans Weinberger

University of Minnesota

Some models for ecological invasions

Nov. 22, Tuesday

Thanks Giving

(No talk)

Nov. 29,Tuesday

Domenico D'Alessandro

Iowa State University

Quantum Symmetries, Cartan Decompositions and Quantum System Identification in Arbitrary Dimensions

 

Dec. 6, Tuesday

Krishna B. Athreya

Iowa State University

Gibbs-Boltzman measures, Entropy maximization, and measure free maringales

 

Abstracts:

Aug. 30, Tuesday 4:10p.m.-5p.m.  Prof. Yangbo Ye, University of Iowa

Title: Prime number theorem for automorphic L-functions

Abstract: Using zero-free regions of L-functions, we will prove Selberg's orthogonality conjecture and prime number theorem for automorphic L-functions for GL(n).

 

Sep. 6th, Tuesday 4:10-p.m.-5p.m. Dr. Yalcin Sarol, Iowa State University

Title: Portfolio optimization in a Black-Scholes market driven by fractional Brownian motion
Abstract:
We consider a portfolio with consumption in a Black-Scholes market where the noise term driving the stock price is given by the fractional Brownian motion, B^H, with Hurst parameter H>1/2, and we solve the classical Merton problem of finding the optimal consumption rate and the optimal portfolio. The interpretation of the integrals with respect to B^H is in the Skorohod sense. Using logarithmic utility functions, we derive formulae for the optimal consumption rate and the optimal portfolio explicitly in the sense that the randomness in these formulae are given only by Wiener type integrals. Therefore, the results stand a good chance of implementation.

 

Sep. 13, Tuesday 4:10p.m.-5p.m. Dr. Raffaele Romano, Iowa State University

Title: The role of complete positivity in open quantum system dynamics

 

Abstract: In this talk the general formalism used to describe the dynamics of an open quantum system is reviewed, in the markovian limit for the time- evolution. The property of complete positivity is particularly important in order to treat consistently systems presenting quantum correlations (i.e. entangled systems). A necessary and sufficient condition for complete positivity of a markovian factorized dynamics is presented, and the physical interpretation discussed.

 

Comments: The first part of the talk will be dedicated to a pedagogical introduction to open system dynamics (the formalism and properties discussed here will be rather standard). The original contribution will be the Theorem discussed in the second part of the talk.

 

Sep. 20, Tuesday 4:10p.m.-5p.m.

Professor Krishna Rajan** Department of Materials Science and Engineering & Institute for Combinatorial Discovery, Iowa State University

Title: Materials  Informatics: A new interface between the mathematics and materials sciences* 

 

Abstract: The role of mathematics in addressing recent advances in computational and experimental materials science is briefly reviewed, including areas such as : minimal surfaces, level set methods and  non linear dynamics to mention just a few. Most of the applications of advanced mathematical tools help to address and model continuum descriptions of materials behavior. In our research we are exploring a very different approach to describe materials properties and predictions;  namely,  an approach driven by discrete multivariate data from which one can develop models and descriptions of materials behavior linking length and time scales. By coupling such information with statistical learning and data mining methods, one can develop powerful and rapid means of modeling and prediction that can significantly advance the pace of materials science research. We provide examples of how such mathematical tools have impacted on materials science research and propose an invitation to the mathematical sciences community for collaborations to help generate the next significant level of integration between mathematics and materials science.

 

* work supported through NSF and ONR

**Director: NSF International Materials Institute-Combinatorial Sciences and Materials Informatics Collaboratory (CoSMIC-IMI)


 

 

Sep.27, Tuesday 4:10-p.m.-5p.m. Dr. Jozsef Balogh, University of Illinois at Urbana-Champaign

Title: “Threshold growth cellular automata: bootstrap percolation.”

Abstract: Cellular automata were introduced by von Neumann after a suggestion of Ulam. A very popular cellular automaton is Conway's `Game of Life'. Bootstrap percolation, a deterministic threshold growth model of cellular automata with random initial condition, was introduced by statistical physicists in the early 1980s.  

In this talk I shall briefly survey the history of bootstrap percolation, and then present some recent results from a number of papers written jointly with B. Bollob\'as, Y. Peres, G. Pete and B. Pittel.

 

Oct. 4, Tuesday 4:10-5p.m.  Professor Fred Goodman University of Iowa

Title:Tangles and algebras.

Abstract: I will discuss some algebras related to braids and links, and their role in representation theory and topology. I will finish by discussing a theorem of Goodman and Hauschild on an algebra of tangles in the solid torus.

 

Oct. 11, Tuesday, Prof. Amy Cohen, Rutgers University

Title:  How far can one push the inverse scattering method?

Abstract:  The cubic Schrodinger equation (cuSch) in one space variable is used to model signals in fiber optics.  It is also amenable to solutions by means of the inverse scattering method, a scheme first introduced for the Korteweg-deVries equation.  Both equations have "soliton" solutions. In the classical application of inverse scattering for cuSch, there is a "mystery hypothesis".  I will try to remove some of that mystery.

 

 

Oct. 25, Tuesday (Miller Lecture) Professor Paul Rabinowitz, University of Wisconsin

Title: Multi-transition solutions for a class of PDEs.

Abstract: A class of equations that can serve as a simple model for phase transition phenomena will be presented. The model possesses a large number of different kinds of solutions which will be described.
 

 

 

Nov. 3 Thursday Prof. Chi-Wang Shu, Division of Applied Mathematics, Brown University (This talk has been canceled.)

Title: Local Discontinuous Galerkin Methods for Dispersive Wave Equations

Abstract: In this talk I will first give a general introduction to the discontinuous Galerkin finite element method and the main technical issues in generalizing this method to solve PDEs with higher order spatial derivatives.  I will then introduce the recent research of designing stable and convergent local discontinuous Galerkin methods for solving various nonlinear dispersive wave equations, including the Kadomtsev-Petviashvili equations and the Zakharov-Kuznetsov equations.  Numerical results will be shown to demonstrate the good qualities of such methods.  This is a joint work with Jue Yan and Yan Xu.

 

Nov. 8, Thursday 4:10p.m. Prof.  Leslie Hogben, Iowa State University
Title: Combinatorial Matrix Theory
Abstract:
Combinatorial matrix theory, encompassing connections between linear algebra, graph theory, and combinatorics, has emerged as a vital area of research over the last few decades, having applications to fields as diverse as biology, chemistry, economics, and computer engineering. This talk will discuss recent results on several problems in combinatorial matrix theory, including algorithms for the computation of
the minimal rank/maximal eigenvalue multiplicity among symmetric matrices described a given graph or sign pattern.

 

Nov. 29, Tuesday 4:10p.m. Prof. Domenico D'Alessandro, Iowa State University

Title:  Quantum Symmetries, Cartan Decompositions and Quantum System Identification in Arbitrary Dimensions

 

Abstract:

Decompositions of Lie groups have been extensively used in control theory to design control algorithms for bilinear, right invariant, systems with state varying on a Lie group. They also play an important role in quantum information theory as they are used to analyze quantum dynamics. Motivated by recent results on entanglement of quantum systems, we clarify the relation between quantum symmetries and Cartan Lie group decompositions. As a consequence, we obtain a novel method to construct a decomposition for unitary operators on a multipartite quantum system starting from decompositions concerning the single subsystems. The resulting decomposition, which we call of the 'odd-even type', contains, as a special case,  the  concurrence canonical decomposition (CCD) presented in entanglement theory. The generalization consists of allowing any possible dimension and different types of Cartan decompositions for the single subsystems. The results are applied to a system theoretic problem of interest in spin dynamics and in particular in nuclear magnetic resonance.

The problem is that of characterizing models of networks of particles with spin, driven by an electro-magnetic field, which are input-output equivalent. These are models which give the same value of the total magnetization for every input field. A complete classification of equivalent models can be obtained in terms of the introduced Cartan decompositions.


 

Dec. 6th, 2005 Tuesday 4:10p.m. Professor Krishna B. Athreya, Iowa State University

Title: Gibbs-Boltzman measures, Entropy maximization, and measure free maringales.

Abstract:

Gibbs-Boltzman (GB)measures arise as those probability measures that maximize relative entropy subject to linear constraints.
In this talk we discuss 1)entropy maximization without using Lagrange multipliers,
2)weak convergence of GB measures and 3)apply it to measure free martingales.
No background in probability theory will be assumed.

 

 

 

Contact Information:

boushaba@iastate.edu or linglong@iastate.edu