Schedule of Talks

Prof. Dongho Chae

Abstracts:

Sep. 9, Thursday, 4:10p.m. Professor Yinyu Ye, Department of Management Science and Engineering, Stanford University

Title: Semidefinite programming for ad hoc wireless sensor network localization and other Euclidean geometry problems

Abstract:
We describe a distributed and decomposed semidefinite programming (SDP) method for solving localization problems that arise from ad hoc wireless sensor network and other Euclidean distance geometry. The SDP problem is set up so as to minimize the error in sensor positions to fit distance measures. Observable gauges are developed to check the quality of the point estimation of sensors or to detect erroneous sensors. The performance of this technique is highly satisfactory compared to other techniques.  Very few anchor nodes are required to accurately estimate the position of all the unknown nodes in a network. Also the estimation errors are minimal even when the anchor nodes are not suitably placed within the network or the distance measurements are noisy. We also use the SDP duality and interior-point algorithm theories to prove that SDP localizes any network or graph that has ``unique''  sensor positions to fit given distance measures.
 

Sep. 17, Thursday, 4:10p.m. Professor Kira Adaricheva , Department of Mathematics, Harold Washington College

Title: On some problems associated with convex geometries

Abstract:
In this talk we introduce a general notion of a convex geometry, as a closure system with the anti-exchange axiom. We provide several examples of convex geometries that emerge in different mathematical context. Then we concentrate on two particular problems that involve convex geometries. One of them is the Jamison problem with its origin in plane geometry, the other is the study of choice functions with path independence that model the consumer behavior in microeconomics.

Sep. 21, Tuesday, 4:10p.m. Professor Geoffrey Mason, Department of Mathematics, University of California at Santa Cruz

Title: What is a quantum field?

Abstract:
In recent years, quantum conformal field theory has become a hot mathematical topic. I'll try to explain how mathematicians deal with this new type of symmetry.
 

Sep. 28, Tuesday, 4:10p.m. Professor Herbert Hethcote, Department of Mathematics, University of Iowa

Title: A predator-prey model with infected prey

Abstract:
A predator prey model with logistic growth in the prey is modified to include an SIS parasitic infection in the prey with infected prey being more vulnerable to predation. Thresholds are identified which determine when the predator population survives and when the disease remains endemic. For some parameter values the greater vulnerability of the infected prey allows the predator population to persist, when it would otherwise become extinct. Also the predation on the more vulnerable prey can cause the disease to die out, when it would remain endemic without the predators.

Sep. 7, October, 4:10p.m. Professor Richard S. Laugesen, Department of Mathematics, , University of Illinois (Urbana-Champaign)

Title: Lord Rayleigh's Conjecture about Vibrating Plates

Abstract:
In 1877, Lord Rayleigh was led by intuition and experimental evidence to conjecture that among all vibrating plates having the same area, and with their edges being clamped, the circular plate should have the lowest fundamental tone. In his words: "When the edges are clamped, the form of gravest pitch is doubtless the circle". More than one hundred years later, this conjecture was proved by Nadirashvili. But the problem remains open in dimensions 4 and hgher. Note: I wll assume some familiarity with the one dimensional wave equation for a vibrating string (such as covered in an undergraduate course), but will otherwise aim at a general mathematical audience.

October. 26, Tuesday, 4:10p.m.
Professor Eric Carlen, Department of Mathematics, Georgia Institute of Technology  

Title: The proof and use of certain entropy inequalities

Abstract:

Let $\rho$ be a probability density with respect to some measure $\mu$. The entropy of $\rho$ is the quantity   $S(\rho) = \int \rho \ln \rho{\rm d}\mu$. Inequalities for the entropy play an important role in information theory, statistical mechanics and partial differential equations. This lecture will present some recent entropy inequalities, together with some that are now classical, explaining where they come from, and what they are good for.
 

November 2, Tuesday, 3:30p.m. Professor Ken Ono  Department of Mathematics, University of Wisconsin at Madison

Title: Number Theory: Partitions and the Legacy of Dyson and Ramanujan

Abstract:

At first glance the stuff of partitions seems like child's play:

                   4 = 3+1 = 2+2 = 2+1+1 =1+1+1+1.

Therefore, there are 5 partitions of the number 4. But (as happens in Number Theory) the seemingly simple business of counting the ways to break a number into parts leads quickly to some difficult and beautiful problems. Partitions play important roles in such diverse areas of mathematics and Combinatorics, Lie Theory, Representation Theory, Mathematical Physics, and the theory of Special Functions, but we shall concentrate here on their role in Number Theory. We shall give an account of the impact of Leonhard Euler, Freeman Dyson and Srinivasa Ramanujan on the subject, and describe some of the recent advances in the subject.

November 9, Tuesday, 4:10p.m. Professor Pam Cook, Department of Mathematics, University of Delaware

Title: The human eye tear film: Modeling and analysis

Abstract:

Problem formulation, modeling, and resultant fits to data are presented of a single layer thin complex fluid film representing the human eye tear film.
The model parameters are fit to viscometric shear data of extracted tear fluid and the resultant system is analyzed under drainage and blink conditions. 
The lubrication approximation is examined and its validity is analyzed in drainage and blink/"coating" flows.  Capillarity at the  free surface and as
well gravitational effects are considered.  Asymptotic, analytic and computational results are presented.  The work is important for understanding the behavior of the tear film in both normal and "dry" eyes

November 16, Tuesday, 4:10p.m.Professor Hailiang Liu, Department of Mathematics at Iowa State University

Title:Geometric Methods for Computing High-Frequency Waves

Abstract:

In this talk we present a novel level set method for computational high frequency wave propagation in dispersive media, with an application to linear Schr\"{o}dinger equations with highly oscillating initial data. In this context we also discuss the new development on computing multi-valued position density and other physical observables.

November 30, Tuesday, 4:10p.m. Professor Dongho Chae , Department of Mathematics,

Abstract

In this talk we present results of the global in time regularity for the 2D Boussinesq system with  either the zero diffusivity or  the zero viscosity. 

We also have that as diffusivity (viscosity) goes to zero the solutions of the fully viscous equations converges strongly to those of zero diffusion (viscosity) equations.