Iowa State University Mathematics Colloquium Fall 2007

 

Location: Carver 150, Time: Tuesday 4:10-5p.m. 

 

 

 

• Previous semesters achieve: Fall 2004,  Spring 2005,  Fall 2005,  Spring 2006, Fall 2006, Spring 2007
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Abstracts:

Sep. 4, Tuesday, Prof. Krishna Athreya, Iowa State University

Title: Entropy and Martingales

Abstract: In this talk the notions of entropy and martingales will be defined .In the first half a number of known results will be presented. The second half will be devoted to current ongoing work  on measure free martingales and the Gibbs- Boltzman entropy maximisation  measures. This is joint with M.G. Nadkarni of Mumbai Universirty, India.

 

Sep. 18, Tuesday, Prof. Domenico D'Alessandro, Iowa State University

Title: An open problem in quantum information theory described as a problem in linear algebra

Abstract: One of the standard open problems in quantum information theory is to give operational criteria to decide whether or not a quantum state is entangled. This very important problem has been solved completely only for low dimensional cases while for higher dimensional cases criteria exist which are only sufficient for entanglement but not necessary. This poses the question of the relation between different criteria. In this talk I will present two such tests and pose the question about which criterion is more powerful. In all the examples I have treated the two tests perform in exactly the same way although a proof of their equivalence is missing.
        I will present the talk using only linear algebra language so as to make it accessible to a wide audience and in particular to people not familiar with the quantum theory. The only pre-requisite to appreciate this open problem is a working knowledge of Linear algebra.

 

Sep. 27, Thursday Prof. Gregory Wene, The University of Texas at San Antonio
Title: Semifields, Geometry and Coding Theory
Abstract: A finite division ring with unit element is called a semifield.While infinite not associative division rings have been known since the 1840's, the first examples of finite, not associative, semifields were given by L E. Dickson in 1905. Finite semifields are very close to fields, the restrictions that the multiplication be associative and commutative being relaxed. However, the algebraic properties very wildly from that  of fields.

Oct. 2, Tuesday, Prof. Leif Jorgensen,  Aalborg University Denmark
Title: Directed strongly regular graphs
Abstract If a 3-dimensional matrix algebra contains the matrices I and J and is closed under both ordinary and entry-wise multiplication (but not necessarily transposition) then it is the adjacency algebra of a (directed) graph called a directed strongly regular graph. In combinatorial terms this means that the number of paths of length 2 from a vertex x to a vertex y depends only on whether there is an edge directed from x to y.

Oct. 9, Tuesday, Prof. Chris Godsil, University of Waterloo
Title: Association schemes and type-II matrices
Abstract:  Type-II matrices are a class of matrices that were used by Vaughan Jones to construct interesting new invariants of knots and links, known as spin models. They are closely related to a number of combinatorial objects, and in particular to association schemes. I this talk I will develop this connection, and discuss the open problems that result.

Oct. 16, Tuesday, Prof. Ivan Correa,  Metropolitan University of CS of the Education
Title: Semiprimality, Solvability and Nilpotency in Algebras Satisfying X(YZ)=Y(ZX)
Abstract:  We study cyclic algebras, that is algebras satisfying the polynomial identity x(yz)=y(zx). We prove that every semiprime cyclic algebra is associative and commutative and that every cyclic right-nil algebra is solvable. We find sufficient conditions for the nilpotency of cyclic right-nilalgebras. Moreover, we prove that when a cyclic algebra is flexible, that is, satisfies the identity (xy)x=x(yx), the products of five elements are associative and commutative. As consequence of this, we get that when such an algebra is a nilalgebra of bounded nilindex, it is nilpotent.

Oct. 23, Tuesday, Prof. Alexander Kurganov, Tulane University
Title: Non-Oscillatory Central Schemes -- a Powerful Black-Box-Solver for Hyperbolic PDEs
Abstract: I will first give a brief description of finite-volume, Godunov-type methods for hyperbolic systems of conservation laws. These methods consist of two types of schemes: upwind and central. My lecture will focus on the second type -- non-oscillatory central schemes.
        Godunov-type schemes are projection-evolution methods. In these methods, the solution, at each time step, is interpolated by a (discontinuous) piecewise polynomial interpolant, which is then evolved to the next time level using the integral form of conservation laws. Therefore, in order to design an upwind scheme, (generalized) Riemann problems have to be (approximately) solved at each cell interface. This however may be hard or even impossible.
        The main idea in the derivation of central schemes is to avoid solving Riemann problems by averaging over the wave fans generated at cell interfaces. This strategy leads to a family of universal numerical methods that can be applied as a black-box-solver to a wide variety of hyperbolic PDEs and related problems. At the same time, central schemes suffer from (relatively) high numerical viscosity, which can be reduced by incorporating of some upwinding information into the scheme derivation -- this leads to central-upwind schemes, which will be presented in the lecture.
        At the end of the talk, I will show a number of recent applications of the central schemes.

Nov. 6, Tuesday, Prof. Mathieu Merle, University of British Columbia
Title: Voter, Lotka-Volterra models and super-Brownian motion
Abstract: In a variety of contexts, such as statistical physics, biology and even sociology, one wishes to modelize the evolution of a system of particles, or individuals. To this motivation correspond discrete and continuous mathematical objects, which are also studied for their own sake. Voter and Lotka-Volterra models can be both interpreted as discrete models for competition species as well as representing the spread of an opinion. Super-Brownian motion is a model for population undergoing both spatial displacement and a continuous branching phenomenon.
        Recently, it was shown by Bramson, Cox, Durrett, Le Gall and Perkins that these objects are closely related, as super-Brownian motion appears at the scaling limit of both voter and Lotka-Volterra models, in dimension greater than two.
        We will see how know properties of super-Brownian motion can be exploited in order to, on the one hand, get asymptotic results for the hitting probabilities of the voter model, and, on the other hand, following the recent work of Cox and Perkins, obtain results on survival and coexistence for the Lotka-Volterra model.

Nov. 9, Friday, Prof. Ofer Zeitouni, University of Minnesota and Weizmann Institute
Title: Some challenges in the study of motion in random media
Abstract: The study of motion in disordered media has a long history, with ties to homogenization theory, involving techniques from both PDE's and probability theory. I will focus in this talk on a simple to describe model of motion in random media, in which a nearest neighbor random walk is started on the sites of the d-dimensional lattice, with transition probabilities that depend on the site the walk visits. This simple to describe model presents many challenges, and I will try to explain some of these as well as describe recent advance.

Nov. 13, Tuesday, Prof.  Li Guo, Rutgers University at Newark
Title: Rota-Baxter algebras, shuffle products and Birkhoff decomposition
Abstract: The Rota-Baxter operator is an abstraction of the integral operator characterized by the integration by parts formula. Its study originated from the work of the mathematician Glenn Baxter in probability in 1960 and is related to the Yang-Baxter equation named after the well-known physicists. Free Rota-Baxter algebras are constructed by a generalized shuffle product. The decomposition in Rota-Baxter algebras is applied to renormalizations in quantum field theory and multiple zeta values. We will survey these aspects in this talk.

Nov. 27, Tuesday, Prof. Marko Djordjevic, Ohio State University
Title: Quantitative modeling and bioinformatics of gene transcription
Abstract: The talk will address both mathematical modeling of biological systems and biophysics approach to bioinformatic problems, through research examples arising in gene transcription. The first part of the talk will address how RNA polymerase is initiating gene transcription. The first quantitative model for the open complex formation (the first step in transcription initiation) will be presented, and shown to be in a good correspondence with experimental data. In the second part of the talk, the problem of detection of transcription factor binding sites in genomic DNA will be addressed. It will be shown how physical modeling of the relevant biological experiments can significantly improve both the experimental design and bioinformatic procedure for inferring protein-DNA interaction parameters.

December. 4, Tuesday, Prof. Margo Levine, James Franck Institute, University of Chicago
Title: Modeling the Self-Assembly of Quantum Dots in Thin Solid Films
Abstract: The fabrication and properties of semiconductor quantum dots has received significant attention in recent years due to their potential application in a wide range of nanoscale integrated systems (qubits, diodes, etc). One feature of quantum dots is that they can form spontaneously, or self-assemble, as the result of an instability when a thin solid film is deposited onto a solid substrate. We investigate two distinct mechanisms for this instability, one associated with anisotropic surface energy and the other with epitaxial stress. In both cases, we show that wetting interactions between the film and the substrate change the instability spectrum from long-wave to short-wave and may lead to the formation of stable regular arrays of quantum dots. We study the evolution of the film surface near the short-wave threshold, and we determine criteria for the stability of the dot arrays.

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Contact Information:

boushaba@iastate.edu or linglong@iastate.edu