## Colloquium: Friday, May 6, 2011

**Spectral Theory and Weyl Asymptotics for Perturbed Krein Laplacians**

Fritz Gesztesy (University of Missouri)

2:00 pm / CH 445

## Colloquium: Friday, April 22, 2011

**Hardy's and related inequalities**

Michael Loss (

**Georgia Institute of Technology**)

2:00 pm / CH 445

Abstract.

## Colloquium: Friday, April 15, 2011

**The Ray-Singer conjecture for singular manifolds**

Xianzhe Dai (

**University of California, Santa Barbara**)

2:00 pm / CH 445

Abstract. The Reidemeister torsion (R-torsion) is a combinatorial invariant introduced by Reidemeister in 1935. It is a secondary invariant associated to the Euler characteristic and is the first topological invariant which distinguishes homotopy equivalent spaces. The analytic torsion is introduced by Ray and Singer in the 70's as an analytic analog of the R-torsion. The Ray-Singer conjecture, which is proven independently by Cheeger and Mueller, says that the analytic torsion equals the R-torsion for closed manifolds. Recent interesting application of the Cheeger-Mueller theorem includes detecting torsion homology classes of hyperbolic manifolds. Thus it will be both interesting and desirable to extend it to singular manifolds. We will discuss the recent understanding along this direction.

## Colloquium: Friday, April 1, 2011

**Asymptotic behavior of solutions to the $\sigma_k$-Yamabe equation near isolated singularities**

Yanyan Li (Rutgers Unversity)

2:00 pm / CH 445

Abstract: We present some results on the behavior of positive solutions in a punctured ball of general second order fully nonlinear conformally invariant elliptic equations. We prove that such a solution, near the puncture, is asymptotic to some radial solution of the same equation in the punctured Euclidean space. This is a joint work with Z.C. Han and E. Teixeira.

## Colloquium: Friday, March 25, 2011

**Mathematical Issues in Visual Transduction**

Emmanuele DiBenedetto (Vanderbilt University)

2:00 pm / CH 445

Abstract: Visual transduction is the process by which photons of light are converted into electrical signals by diffusion of the second messengers Calcium and cGMP (cyclic guanosine monophosphate) in the cytoplasm of the Rod Outer Segment (ROS). A mathematical model of such a transduction is presented, that accounts for the layered geometry of the Rod Outer Segments and the incisures born by the discs. The model provides an explanation for the role of incisures, believed as evolutionary residues. The model also explains the biological/structural reasons for the high filelity of the photoresponse, despite the fact that reception of photons of light is a process with several random components.

## Colloquium: Friday, March 4, 2011

**Topological Models for Julia Sets**

Clinton P. Curry (Stony Brook University)

2:00 pm / CH 445

Abstract: The dynamics of complex polynomials is concentrated on a fully invariant subset of the plane called the Julia set. It is of intrinsic interest to describe the Julia set topologically. I will describe recent advances in terms of what we call finest models, and describe difficulties in extending our understanding to more general kinds of functions (for example, quotients of polynomials). The topics discussed will include joint work with Alexander Blokh, John C. Mayer, and Lex Oversteegen of UAB, and E. D. Tymchatyn of the Universoty of Saskatchewan.

## Colloquium: Friday, February 25, 2011

**Lieb-Robinson Bounds and Applications**

Robert Sims (University of Arizona)

2:00 pm / CH 445

Abstract: Locality is an essential tool in analyzing various physical systems. For non-relativistic systems generated by a Hamiltonian dynamics, it is well-known that the time evolution does not generally preserve local structures, i.e., there is no strict equivalent to a finite speed of light. In 1972, Lieb and Robinson demonstrated that the dynamics associated with certain non-relativistic systems has an approximate local structure. In particular, such systems have an associated, finite group velocity. We will discuss this result, several recent generalizations, and a variety of interesting applications.

## Colloquium: Friday, February 18, 2011

**Special Functions and Integrable Systems**

Alexander Its (Indiana University-Purdue University Indianapolis)

2:00 pm / CH 445

Abstract: The recent developments in the theory of integrable systems have revealed its intrinsic relation to the theory of special functions. Perhaps the most generally known aspects of this relation are the group-theoretical, especially the quantum-group theoretical, and the algebra-geometrical ones. In the talk we will discuss the analytic side of the Special Functions-Integrable Systems connection. This aspect of the relation between the two theories is less known to the general mathematical community,although it goes back to the classical works of Fuchs, Garnier and Schlesinger on the isomonodrony deformations of the systems of linear differential equations with rational coefficients. Indeed, the monodromy theory of linear systems provides a unified framework for the linear(hypergeometric type) and nonlinear (Painlev\'e type) special functions and, simultaneously, builds a base for the new powerful technique of the asymptotic analysis - the Riemann-Hilbert method. In this survey talk, which is based on the works of many authors spanned over more than two decades, the isomonodromy point of view on special function will be outlined. We will also review the history of the Riemann-Hilbert method as well as its most recent applications in the theory of orthogonal polynomials and random matrices.

## Colloquium: Friday, February 4, 2011

**The Liouville theorem for subharmonic functions, and generalizations**

**James Serrin** (University of Minnesota)

2:00 pm / CH 445

**Abstract. 'The standard Liouville theorem states that every bounded entire complex analytic function is a constant. We discuss various classical improvements of this result, including whether it remains true for harmonic and subharmonic functions. This leads to a quite general final result for subsolutions of a class of elliptic variational equations.'**

## Colloquium: Friday, January 21, 2011

**Productsets of large sets in amenable groups**

Alexander Fish (University of Wisconsin)

2:00 pm / CH 445

## Colloquium: Friday, January 14, 2011

**Manifolds with pinched flag curvature**

Lei Ni (University of California, San Diego)

2:00 pm / CH 445

## Colloquium: Friday, January 13, 2011

**A shape-based method for determining protein binding sites in a genome**

Valerie Hower (University of California - Berkeley)

9:30 am / CH 458

## Colloquium: Monday, January 10, 2011

**Scaling limits of random walks in random scenery: local time and indicator fractional stable motions**

Paul Jung (Sogang University)

10:00 am / CH 458

## Colloquium: Friday, January 7, 2011

**Novel techniques for acoustic and electromagnetic field manipulations and their applications**

Daniel Onofrei (University of Utah)

10:00 am / CH 458

## Colloquium: Friday, November 19, 2010

**Complete Hypersurfaces of Constant Curvature in Hyperbolic Space**

Bo Guan (Ohio State University)

2:00 pm / CH 445

Abstract. 'We discuss the problem of finding complete hypersurfaces in hyperbolic space with asymptotic boundary at infinity determined by a symmetric function of principal curvatures. We shall use the upper half space model and method of partial differential equations to prove exsitence results. Results described in this talk are joint work with Joel Spruck and Marek Szapiel.'

## Colloquium: Friday, November 12, 2010

**Gluing constructions for minimal surfaces**

Nicos Kapouleas (Brown University)

2:00 pm / CH 445

Abstract. 'I will concentrate on doubling and desingularization constructions: I will first discuss doubling constructions for the Clifford torus and the equatorial two-sphere in the round three-sphere. In doubling constructions minimal surfaces are constructed resembling two copies of the given minimal surface joined by many small catenoidal bridges. I will then discuss desingularization constructions where minimal surfaces are constructed by replacing the intersection curves of minimal two-surfaces in a Riemannian three-manifold with handles modeled after the singly periodic Scherk surfaces and then perturbing to minimality. Finally I will discuss some applications and open questions for closed embedded minimal surfaces in the three-sphere.'

## Colloquium: Friday, November 5, 2010

**Some applications of heat equation method to the Ricci flow**

Qi Zhang (University of California, Riverside)

2:00 pm / CH 445

Abstract. 'We start with some old ideas involving heat equation such as monotonicity of entropy and energy. Then we discuss how these are applied by Perelman and others to study 3 dimensional Ricci flow. Some concrete and potential applications to high dimensional Ricci will also be addressed.'

## Colloquium: Friday, October 29, 2010

**The Kahler Ricci flow on Toric Fano surface**

Bing Wang (Princeton University)

2:00 pm / CH 445

## Colloquium: Friday, October 22, 2010

**Some new geometric evolution equations**

Jeff Streets (Princeton University)

2:00 pm / CH 445

Abstract. 'After giving a brief history of the application of geometric flows in geometry and topology, I will discuss two new such flows. The first is the gradient flow of the L^2 norm of curvature, which can be used to show a weak type of "sphere theorem." The second is a geometric flow on complex, non-Kahler manifolds. After discussing a recently discovered connection between this flow and mathematical physics, I will discuss some regularity theorems and the potential application to understanding the classification of nonKahler surfaces.'

## Colloquium: Friday, October 8, 2010

**Diffusion of waves in a random environment: problems and results**

Jeffrey Schenker (Michigan State University)

2:00 pm / CH 445

## Colloquium: Friday, October 1, 2010

**Circle Decompositions of Surfaces**

Nandor Simanyi (UAB)

2:00 pm / CH 445

## Colloquium: Friday, September 24, 2010

**Measure of Buried Points in Julia Sets**

John Mayer (UAB)

2:00 pm / CH 445

## Colloquium: Friday, September 17, 2010

**Time reversal method in Thermoacoustic tomography**

Yulia Hristova (IMA and Texas A&M)

2:00 pm / CH 445

## Colloquium: Friday, September 10, 2010

**Modeling Risk and Uncertainty – Applications in Power Markets and Trading**

Jeff Baker (Southern Company)

2:00 pm / CH 445

Abstract. 'Economically running a reliable power system depends on a variety of highly volatile variables. These include weather, fuel costs, generator availability, legislation, and many others. Volatility introduces risk and uncertainty when planning for the short term (tomorrow) as well as the long term (next 5-20 years). The physical characteristics of power also present a number of challenges when valuing power as a tradable commodity, as opposed to other commodities such as wheat, corn, oil, etc. In this talk I will present some of the models and tools Southern Company’s Fleet Operations and Trading use to approach these problems. I will also give some insight about what it is like to be a mathematician in industry.'## Colloquium: Friday, August 20, 2010

**Exit times of diffusions with incompressible drifts**

Andrej Zlatos (University of Wisconsin)

2:00 pm / CH 445

Abstract. 'We consider the influence of an incompressible drift on the expected exit time of a diffusing particle from a bounded domain. Mixing resulting from an incompressible drift typically enhances diffusion so one might think it always decreases the expected exit time. Nevertheless, we show using PDE techniques that in two dimensions, the only simply connected domains for which the expected exit time is maximized by zero drift are the discs.'