Date: August 28, 2008
Speaker: Andrew Booker, University of Bristol, UK
Title: Alan Turing and the Riemann hypothesis

Abstract: Many mathematicians are familiar with Alan Turing as a logician, pioneer of computer science, and even war hero.  Not so many know that he was also a number theorist.  I will describe Turing's interest in the Riemann hypothesis, in a manner accessible to all.

Date: September 10, 2008
Speaker: Richard Askey, National Academy of Sciences
Title: Different Ways to Look at Ptolemy’s Theorem

Abstract:

Date: September 18, 2008 (Joint Math and AMCS)
Speaker: Yang Kuang, Arizona State University
Title: Resource quality in population dynamics and its implications

Abstract: Rising carbon dioxide levels should increase crop yields. But what is their effect on the nutritional value of our food? It is known that elevating the level of carbon dioxide can significantly reduce the leaf nitrogen content and hence leaf mites’ reproduction and renders pesticide unnecessary in greenhouse vegetable production This rises the question of how resource quality impact the population dynamics in general. The challenge is how to model quality in a succinct and plausible way. Mathematical biologists have built on variants of the Lotka–Volterra equations and in almost all cases have adopted the physical science’s single-currency (energy) approach to understand population dynamics. However, biomass production is essentially a mass transfer process that requires more than just energy. It is crucially dependent on the chemical compositions of both the consumer species and food resources. In this talk, we explore how depicting organisms as built of more than one thing, for example, C to represent energy, and an important nutrient, such as P (or N), to represent quality, results in qualitatively different and realistic predictions about the resulting dynamics.

Date: October 2, 2008 (Joint Math and AMCS)
Speaker: Ray P.S. Han, Beijing University, China
Title: Modeling the Size-Dependent Elastic Properties of Polymeric Nanofibers

Abstract: We present a strain gradient (SG) theory to explain the strongly inverse size dependency between the elastic modulus and fiber diameter in polymeric nanofibers. For centro-symmetric and isotropic materials we showed that the 3 length-scale parameters can be combined into a single parameter that can be used to predict the onset of the size-dependent trend when the fiber diameter is reduced past its critical size. To address the issue of whether SG offers a plausible explanation of the size-dependent behavior we conducted a series of unaxial tensile and static bending tests involving the polycaprolactone nanofibers. Since the elastic modulus is highly sensitive to the fiber diameter, it is necessary to correct the experimental data to account for the lack of circularity in the cross-section of the real fiber. Additionally, we applied the SG model to study the size-dependent elastic properties of polypyrrole nanotubes. By approaching the SG theory from a dynamics point of view, our model is able to capture size-dependent effects in the mechanics of fine-scale materials for both static and dynamic responses.

Date: October 23, 2008
Speaker: Mike Williams, University of California-Santa Barbara
Title: 3-manifolds and surface decompositions

Abstract: This talk will survey the approach of understanding 3-manifolds (spaces that "locally look like" Euclidean 3-space) by studying embedded surfaces contained in them by so-called "cutting and pasting". Two examples are the notions of Heegaard splitting and Dehn surgery. I will define and illustrate these notions and connections between them. I will also explain connections to the theory of knots. This talk will be accessible to a general mathematical audience.

Date: November 7, 2008
Speaker: Joaquin Rivera, Colgate University, Hamilton, NY
Title: Computing the Spreading Speed in STDs Models via Linear Determinacy

Abstract: The talk will cover a SIS model for the spatial-spread of sexually transmitted diseases (STD) among subjects of heterosexual orientation. I will start the talk by presenting some of the previous models that were limited to studying the dynamics of the diseases in non-mobile heterosexually active populations. Then I will discuss the model under consideration which consists of a pair of reaction-diffusion equations for each heterosexually-active population. The discussion will center on predicting how fast the disease spreads to non-infected regions. We were able to predict the spread of the diseases by using techniques from Linear Determinacy; this allowed us to determine the conditions required for the successful invasion of these diseases in a population living under near-endemic conditions. Finally, we also demonstrated that there is a unique spreading speed connecting the two endemic equilibria.

Date: November 17, 2008
Speaker: Xinan Ma, University of Science and Technology of China and Institute for Advanced Studies
Title: Convexity and partial convexity of solutions of elliptic equations

Abstract: Convexity of solutions to elliptic equations is a fundamental issue. In the past we have (mainly joint with Prof. Pengfei Guan) established some constant rank theorems for convex solutions of certain nonlinear elliptic PDE. In this talk I shall present some constant rank theorems for k-convex solutions of elliptic equation, and give some applications to the existence of k-convex solutions of the prescribed the mean curvature equation. This is joint work with Fei Han (USTC,China) and Damin Wu (OSU).

Date: December 11, 2008
Speaker: Niles Johnson
Title: Morita, Picard, Brauer, and Yoneda

Abstract: Morita theory is a wonderful story which begins in classical algebra and develops throughout modern algebraic, categorical, and homotopical settings. In the talk, we describe a unifying perspective on Morita theory in its various forms. From this vantage, we discuss the barriers to generalized Morita theory and explain how the Yoneda lemma in this context gives an improved Morita theorem. Moreover, we will see the general Picard and Brauer groups arising naturally and explain how our perspective on Morita theory sheds both conceptual and calculational light on these objects.

Date: December 18, 2008
Speaker: Prof. Jianya Liu
Title: Linnik's problem for automorphic representations

Abstract: Recently, Linnik's famous theorem on the least prime in an arithmetic progression has been generalized to the context of automorphic representations. I will report some new results in this direction, for example, sign changes of Dirichlet coefficients of automorphic L-functions, and the analytic multiplicity one for automorphic representations.

Date: January 20, 2009
Speaker: Michael Goldberg
Title: "Strichartz Estimates for a Wealth of Schrodinger"

Abstract: The Strichartz estimates are a fundamental family of Lp inequalities governing solutions to the free Schrödinger equation. They decribe the dispersive nature of the evolution -- local concentrations of mass can only exist for a specified finite period of time. The associated function spaces can be used to assess well-posedness and scattering properties of perturbed or nonlinear Schrödinger equations. I will review the efforts to identify other Schrödinger operators on Rn that satisfy the same range of Strichartz estimates as the Laplacian. On the technical side, recent progress is driven by improvements in the underlying harmonic and functional analysis. On the motivational side, specific applications often give rise to operators that fall outside (or at the edge) of our current understanding. I will present the orbital stability of solitons in NLS as one such application. Note: Michael Goldberg is a candidate for our tenure track position in Analysis.

Date: January 21, 2009
Speaker: Keiko Kawamuro
Title:

Abstract: Keiko Kawamuro is a candidate for our tenure track position in topology.

Date: January 22, 2009
Speaker: Ionut Chifan
Title:

Abstract: