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|
Date |
Speaker |
Title (Click on the title of a talk for the abstract if available). |
|
Aug. 30,Tuesday |
Yangbo Yang |
Prime
number theorem for automorphic L-functions |
|
Sep. 6, Tuesday |
Yalcin Sarol |
Portfolio optimization in a Black-Scholes market driven by fractional Brownian motion |
|
Sep. 13, Tuesday |
Raffaele Romano |
The role
of complete positivity in open quantum system dynamics |
|
Sep. 20, Tuesday |
|
Materials Informatics: A new interface
between the mathematical and materials sciences |
|
Sep. 27, Tuesday |
Jozsef Balogh |
|
|
Oct. 4, Tuesday |
Fred Goodman |
|
|
Oct. 6, Thursday |
William Sudderth |
How to
bid for a Pizza: An Introduction to
Stochastic Games (Joint colloquium with dept. of Stat.) |
|
Oct. 11, Tuesday |
Amy Cohen |
How far can one push the inverse
scattering method? |
|
Oct. 18, Tuesday |
Jerome W. Hoffman |
|
|
Oct. 20, Thursday |
Bhaba K. Sarma Indian Institute of
Technology Guwahati |
|
|
Oct. 25, Tuesday |
(Miller Lecture 305 Carver Hall) |
Multi-transition
solutions for a class of PDEs. |
|
Nov. 3, Thursday |
Chi-Wang Shu (This talk was canceled.) |
Local Discontinuous Galerkin
Methods for Dispersive Wave Equations |
|
Nov. 8, Tuesday |
Leslie Hogben |
|
|
Nov. 15, Tuesday |
Hans Weinberger |
|
|
Nov. 22, Tuesday |
Thanks Giving |
(No talk) |
|
Nov. 29,Tuesday |
Domenico D'Alessandro |
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,
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.
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,
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,
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,
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
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.
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,
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.
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,
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,
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,
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: