Seminars and Colloquia by Series

Influence of anti-viral drug treatments on evolution of HIV-1 pathogen

Series
CDSNS Colloquium
Time
Monday, February 9, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Zhilan Feng – Department of Mathematics, Purdue University
Mathematical models are used to study possible impact of drug treatment of infections with the human immunodeficiency virus type 1 (HIV-1) on the evolution of the pathogen. Treating HIV-infected patients with a combination of several antiretroviral drugs usually contributes to a substantial decline in viral load and an increase in CD4+ T cells. However, continuing viral replication in the presence of drug therapy can lead to the emergence of drug-resistant virus variants, which subsequently results in incomplete viral suppression and a greater risk of disease progression. As different types of drugs (e.g., reverse transcriptase inhibitors,protease inhibitors and entry inhibitors) help to reduce the HIV replication at different stages of the cell infection, infection-age-structured models are useful to more realistically model the effect of these drugs. The model analysis will be presented and the results are linked to the biological questions under investigation. By demonstrating how drug therapy may influence the within host viral fitness we show that while a higher treatment efficacy reduces the fitness of the drug-sensitive virus, it may provide a stronger selection force for drug-resistant viruses which allows for a wider range of resistant strains to invade.

Projection and Nyström methods for FIE on bounded and unbounded intervals

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 9, 2009 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Giuseppe Mastroianni – Dept. of Mathematics and Informatics, Univ. of Basilicata, Italy)
In this talk I will show a simple projection method for Fredholm integral equation (FIE) defined on finite intervals and a Nyström method for FIE defined on the real semiaxis. The first method is based the polynomial interpolation of functions in weighted uniform norm. The second one is based on a Gauss truncated quadrature rule. The stability and the convergence of the methods are proved and the error estimates are given.

The field of average tile orientations in random tilings with holes

Series
Combinatorics Seminar
Time
Friday, February 6, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Mihai Ciucu – Indiana University and Georgia Tech
The study of random tilings of planar lattice regions goes back to the solution of the dimer model in the 1960's by Kasteleyn, Temperley and Fisher, but received new impetus in the early 1990's, and has since branched out in several directions in the work of Cohn, Kenyon, Okounkov, Sheffield, and others. In this talk, we focus on the interaction of holes in random tilings, a subject inspired by Fisher and Stephenson's 1963 conjecture on the rotational invariance of the monomer-monomer correlation on the square lattice. In earlier work, we showed that the correlation of a finite number of holes on the triangular lattice is given asymptotically by a superposition principle closely paralleling the superposition principle for electrostatic energy. We now take this analogy one step further, by showing that the discrete field determined by considering at each unit triangle the average orientation of the lozenge covering it converges, in the scaling limit, to the electrostatic field. Our proof involves a variety of ingredients, including Laplace's method for the asymptotics of integrals, Newton's divided difference operator, and hypergeometric function identities.

Introduction to the h-principle

Series
Geometry Topology Working Seminar
Time
Friday, February 6, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Mohammad Ghomi – School of Mathematics, Georgia Tech

Please Note: (Please note this course runs from 3-5 pm.)

h-Principle consists of a powerful collection of tools developed by Gromov and others to solve underdetermined partial differential equations or relations which arise in differential geometry and topology. In these talks I will describe the Holonomic approximation theorem of Eliashberg-Mishachev, and discuss some of its applications including the sphere eversion theorem of Smale. Further I will discuss the method of convex integration and its application to proving the C^1 isometric embedding theorem of Nash.

On the long-time behavior of 2-d flows

Series
School of Mathematics Colloquium
Time
Thursday, February 5, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alexander Shnirelman – Department of Mathematics, Concordia University
Consider the 2-d ideal incompressible fluid moving inside a bounded domain (say 2-d torus). It is described by 2-d Euler equations which have unique global solution; thus, we have a dynamical system in the space of sufficiently regular incompressible vector fields. The global properties of this system are poorly studied, and, as much as we know, paradoxical. It turns out that there exists a global attractor (in the energy norm), i.e. a set in the phase space attracting all trajectories (in spite the fact that the system is conservative). This apparent contradiction leads to some deep questions of non-equilibrium statistical mechanics.

Knots and Open Book Decompositions

Series
Research Horizons Seminar
Time
Wednesday, February 4, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Sinem Celik Onaran – Department of Mathematics, Middle East Technical University
Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will define open book decompositions of 3-manifolds. We will discuss various examples and sketch the proof of Alexander's theorem. Further, we will discuss the importance of the open books in manifold theory, in particular in contact geometry.

Hamiltonian identities for Elliptic PDEs and their applications

Series
PDE Seminar
Time
Tuesday, February 3, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Changfeng Gui – University of Connecticut
In this talk I will present Hamiltonian identities for elliptic PDEs and systems of PDEs. I will also show some interesting applications of these identities to problems related to solutions of some nonlinear elliptic equations in the entire space or plane. In particular, I will give a rigorous proof to the Young's law in triple junction configuration for a vector-valued Allen Cahn model arising in phase transition; a necessary condition for the existence of certain saddle solutions for Allen-Cahn equation with asymmetric double well potential will be derived, and the structure of level sets of general saddle solutions will also be discussed.

Binary Black Hole Simulations - Mission Accomplished(?)

Series
CDSNS Colloquium
Time
Monday, February 2, 2009 - 16:30 for 2 hours
Location
Skiles 255
Speaker
Pablo Laguna – School of Physics, Georgia Tech
I will review results from binary black hole simulations and the role that these simulations have in astrophysics and gravitational wave observations. I will then focus on the mathematical and computational aspects of the recent breakthroughs in numerical relativity that have made finding binary black hole solutions to the Einstein field equations an almost routine exercise.

Pages