
Date Time 
Location  Speaker 
Title – click for abstract 

09/07 1:50pm 
BLOC 628 
Irene Gamba UT Austin 
The Cauchy problem and BEC stability for the quantum BoltzmannCondensation System at very low temperature
We discuss a quantum BoltzmannCondensation system that describes the evolution of the interaction between a well formed BoseEinstein Condensate (BEC) and the quasiparticles cloud. The kinetic model, derived as weak turbulence kinetic model from a quantum Hamiltonian, is valid for a dilute regime at which the temperature of a bosonic gas is very low compared to the BoseEinstein condensation critical temperature. In particular, the system couples the density of the condensate from a GrossPitaevskii type equation to the kinetic equation through the dispersion relation in the kinetic model and the corresponding transition probability rate from pre to post collision momentum states.
We show the wellposedness of the Cauchy problem for the system, find qualitative properties of the solution such as instantaneous creation of exponential tails, and prove the uniform condensate stability related to the initial mass ratio between condensed particles and quasiparticles. This stability result leads to global in time existence of the initial value problem for the quantum BoltzmannCondensation system. 

09/14 1:50pm 
BLOC 628 
Joonhyun La Princeton University 
Global well posedness of 2D diffusive FokkerPlanckNavierStokes systems
In this talk, we prove that there is a unique global strong solution to the 2D NavierStokes system coupled with diffusive FokkerPlanck equation of a Hookean type potential. This system regards a polymeric fluid as a dilute suspension of polymers in an incompressible solvent, which is governed by the NavierStokes equation, and distribution of polymer configuration is governed by the FokkerPlanck equation, where spatial diffusion effects of polymers are also considered. Wellknown OldroydB models can be rewritten in the form of this system. Main conceptual difficulties include multiscale nature of the system. We discuss an appropriate notion for the solution for this multiscale system, and approximation scheme. 

09/21 1:50pm 
BLOC 628 
Ziad Musslimani Florida State University 
PT symmetry, nonlocal integrable models and physical applications
In this talk, we shall review basic concepts related to the mathematics and physics of PT symmetry and nonselfadjoint eigenvalue problems. We shall also discuss recent activities in the newly emerging field of PT symmetric and reverse spacetime integrable nonlocal models.


09/28 1:50pm 
BLOC 628 
Maciej Zworski UC Berkeley 
Magnetic oscillations in a model of graphene
We consider the simplest model for graphene in a magnetic field given by a hexagonal quantum graphs. Using semiclassical methods (with the strength of the magnetic field as the small parameter) we obtain a geometric description of the density of states showing asymmetry seen in physical experiments but not in commonly used perfect cone approximations. That density of states can then be used to see magnetic oscillations such as the de Haasvan Alphen effect. Joint work with S Becker. 

10/05 1:50pm 
BLOC 628 
Lior Alon Technion  Israel Institute of Technology 
Nodal and Neumann count statistics for quantum graphs
In this talk I will briefly go over the definitions and results from the work on the nodal count statistics on quantum graphs. Then I will introduce the concept of Neumann count, and properties of Neumann domains such as the spectral position of the restricted eigenfunction and analogous property to the area to length ratio (isoperimetric parameter). I will then state the results regarding the existence and symmetry of the probability distributions of the latter properties.
If time allows I will present a simple but powerful result regarding the edge lengths dependence of the nodal and Neumann distributions for edge transitive combinatorial graphs, and I will finish with our latest results, showing that the nodal distributions for two specific graphs families converge to Gaussian distributions as the the number of edges grows to infinity.
This talk is base on a joint work with R. Band (Technion) and G. Berkolaiko (Texas A&M). 

10/19 1:50pm 
BLOC 628 
Mathew Johnson University of Kansas 
On the Stability of Roll Waves
Rollwaves are a well observed hydrodynamic instability occurring in inclined thin film flow, often mathematically described as periodic traveling wave solutions of either the viscous or inviscid St. Venant system. In this talk, I will discuss recent progress concerning the stability of both viscous and, if time allows, inviscid rollwaves in a variety of asymptotic regimes, including near the onset of hydrodynamic instability and largeFroude number analysis. This is joint work with Blake Barker (BYU), Pascal Noble (University of Toulouse), L. Miguel Rodrigues (University of Rennes), Zhao Yang (IU) and Kevin Zumbrun (IU). 

10/26 1:50pm 
BLOC 628 
Dylan Allegretti University of Sheffield 
Categorified canonical bases and framed BPS states
In a famous paper from 2006, Fock and Goncharov introduced a moduli space of framed PGL(2,C)local systems on a surface with boundary. This moduli space has the structure of a cluster variety, and the algebra of regular functions on this cluster variety has a canonical vector space basis. In this talk, I will describe a family of graded vector spaces which categorify Fock and Goncharov's canonical basis. In certain cases, these vector spaces arise as the cohomology of moduli spaces of stable quiver representations as predicted by the physics of BPS states in N=2 field theories. 

11/02 11:00am 
BLOC 628 
Anton Dzhamay University of Northern Colorado 
Geometry of Discrete Integrable Systems
Many interesting examples of discrete integrable systems can be studied from the geometric point of view. In this talk we will consider two classes of examples of such system: autonomous (QRT maps) and nonautonomous (discrete Painlevé equations). We introduce some geometric tools to study such systems, such as the blowup procedure to construct algebraic surfaces on which the mappings are regularized, linearization of the mapping on the Picard lattice of the surface and, for discrete Painlevé equations, the decomposition of the
Picard lattice into complementary pairs of the surface and symmetry sublattices and construction of a binational representation of affine Weyl symmetry groups that gives a complete algebraic description of our nonlinear dynamic. If time permits, we also explain the relationship between this picture and classical differential Painlevé equations.


11/16 1:50pm 
BLOC 628 
Jari Taskinen University of Helsinki 
Structure and existence of gaps of essential spectra of elliptic boundary problems in periodic waveguides
We review some recent joint works with Sergei Nazarov and others concerning spectral elliptic boundary value problems in periodic waveguides. We consider the structure of the essential spectrum e.g. for the Neumann Laplacian in the case of a doubly periodic perforated plane subject to periodic or nonperiodic, noncompact perturbations. We also deal with the existence, number and position of spectral gaps in the case of the elasticity and piezoelectricity systems in waveguides with thin structures. 