Time: 1:40-2:40 pm Wednesdays
Room: PSA 102
(unless otherwise specified)

DATE

SPEAKER

TOPIC/ABSTRACT

January 18 Time 4:00pm PSA 206     

  Jeff Hoffstein
(Brown University)
         

Title:  Public key Cryptograpghy, Lattice and NTRU    

Abstract:
I'll give a brief survey of public key cryptography, from ancient history (the mid 1970's) to the present day. In particular, I'll concentrate on the interesting possibilities for cryptography offered by lattices, and give a description and analysis of the NTRU public key cryptosystem.    

January 19 Time 2:30pm PSA 107     

  Jill Pipher
(Brown University)
         

Title:  The Dirichlet Problem for the Second Order Divergence or Nondivergence form elliptic equations  

Abstract: 
I will discuss L^p solvability of the Dirichlet problem for second order elliptic divergence form and nondivergence form operators with rough coefficients. In this work, which is joint with M. Dindos and S. Petermichl, we impose a Carleson measure condition on the coefficients, a condition which arises naturally from a change of variables.  

January 31    

  S. Roudenko
(Math. & Stat., ASU)
  

Title:Blow Up Phenomenon in the Nonlinear Schrodinger Equations     

Abstract: I will make an overview of the nonlinear Schrodinger Equations (NLS) with finite time existence solutions (called blow ups). In particular, I will concentrate on (focusing) NLS with cubic nonlinearity in 2 and 3 dimensions and discuss "mass" concentration results and the threshold for solutions with H^1 initial data for global existence and finite time blow up   

February 14, PSA 206
    

  K. Stavrakidis
(Technical University Darmstadt, Germany)
  

Title: L^p-solutions of the magnetohydrodynamic equations      

Abstract:   

February 16, PSA 206 *
(joint with Computational Math seminar)    

  Fernando Carreon
(Math., UT Austin)
  

Title: Singular limits of the KPP equation in an infinite cylinder.      

Abstract: I'll discuss the asymptotic behavior of a reaction diffusion equation of KPP type with Neumann boundary conditions containing a small parameter. The solutions to this equation converge to the indicator function of a set G as the small parameter goes to zero. The set G can be characterized through the unique viscosity solution of a variational inequality involving a Hamilton-Jacobi equation.    

February 19, PSA 308*
    

  Matthias Hess
(Technical University Darmstadt, Germany)
  

Title: Stability of the Ekman spiral for L^2-perturbations      

Abstract: Abstract: We look at the well-known explicit stationary solution to the Navier Stokes equations including the Coriolis force called Ekman spiral. Using methods of operator theory we prove stability of the Ekman spiral for perturbations in L^2 in case of small Reynolds numbers. Furthermore we provide polynomial decay rates for weak solutions of the perturbed problem depending on the initial value.   

February 21    

  Justin Holmer
(Math., U California at Berkeley)
  

Title: Soliton interaction with a delta function potential     

Abstract: We study the Gross-Pitaevskii equation with a delta function potential with coupling constant $q$, and consider an incoming soliton with velocity $v$. We present both analytical and numerical results showing the following. First, for large incoming velocity $v$ and a repulsive potential $q>0$, the soliton is split into a transmitted component and a reflected component, each of which can be quantified and whose subsequent evolution can be described. Next, we consider the case of $q$ small and of either sign, and consider an incoming soliton with small velocity $v$. We show that up to time $(|q| + v_0^2 )^{-\frac12} \log(1/|q|)$ the bulk of the solution is a soliton evolving according the classical dynamics of a natural effective Hamiltonian, $(\xi^2 + q\sech^2 x )/2$   

March 7    

  Nader Masmoudi
(Courant Institute, NYU)
  

Title: Infinite Time Aggregation for the Critical Patlak-Keller-Segel model in $\RR^2$.     

Abstract: The Patlak-Keller-Segel (PKS) model describes the collective motion of cells which are attracted by a self-emitted chemical substance. The long time behavior depends on the total mass which is assumed here to be conserved. It was conjectured by S. Childress and K. Percus that in two space dimensions there is a threshold number above which there is a chemotactic collapse.
One can prove that if the initial mass is below a critical mass 8 pi then the solution is global and spreads when t goes to infinity. If the initial mass is above the critical mass 8 pi then there is blow up in finite time. For the critical mass 8 pi, there is infinite time aggregation. One of the main tools in proving these results is the use of the free-energy of the system combined with a Logarithmic Hardy-Littlewood-Sobolev inequality with a sharp constant.
We will also discuss the derivation of the model from kinetic models and show some numerics.    

March 14    

  G. Seregin
(Math. Institute, St Petersburg, Russia and Dept. of Math., U. of Minnesota)
  

Title: A sufficient condition of regularity for axially symmetric solutions to the Navier-Stokes equations     

Abstract: In the talk, I will discuss a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. The condition is an axially symmetric analog of the so-called $L_{3,\infty}$-case in the general local regularity theory   

April 4    

  Christoph Walker
(Vanderbilt University)
  

Title: Global well-posedness of a haptotaxis model with spatial and age structure     

Abstract: A system of non-linear partial differential equations modeling tumor invasion into surrounding healthy tissue is analyzed. The model focuses on key components involved in tumor cell migration and takes into account cell motility and haptotaxis, that is, the directed migratory response of tumor cells to the extracellular environment. Individual cell processes are modeled according to cell age. The equation for the tumor cell density thus incorporates second-order (parabolic) terms representing diffusion and taxis as well as a first-order (hyperbolic) part due to cell aging. Global existence and uniqueness of non-negative solutions is shown.    

April 25    

  Horst Thieme
(Math. & Stat, ASU)
  

Title: Bounded semivariation, differentiability of convolutions, and the nonhomogeneous Cauchy problem      

Abstract:    

May 2    

  Jason Newport
(Dept. of Math., U. of Arizona)
  

Title: Solutions to the Nonlinear Schrodinger Equation with Dirac Mass Initial Data     

Abstract: We will consider the defocussing nonlinear Schrodinger equation with Dirac mass initial data. We will start with a brief introduction to the scattering theory associated with the NLS equation, and a formal extension of the theory to handle Dirac masses. The bulk of the talk will be on the Riemann Hilbert analysis that gives us an asymptotic description of the solutions. Time permitting we will discuss properties of our solutions.