
Date Time 
Location  Speaker 
Title – click for abstract 

09/06 1:50pm 
BLOC 302 
Qiaochu Ma Texas A&M University 
Mixed quantization and quantum chaos
Quantum Ergodicity (QE) is a classical topic in quantum chaos, it states that on a compact Riemannian manifold whose geodesic flow is ergodic, the Laplacian has a densityone subsequence of eigenfunctions that tends to be equidistributed. In this talk, we present a uniform version of QE for a certain series of unitary flat vector bundles. The key technique involves combining semiclassical and geometric quantizations. The holonomy of flat bundles provides fascinating geometrical phenomena. 

09/20 1:50pm 
BLOC 302 
Xueyin Wang Texas A&M University 
Spectral analysis of nonselfadjoint quasiperiodic Schr\"odinger operators
One of the main challenges in studying nonselfadjoint operators is the lack of a spectral theorem. By applying Avila’s global theory, we derive new spectral and isospectral results for nonselfadjoint quasiperiodic Schrödinger operators. This presentation is based on joint work with Zhenfu Wang, Jiangong You, and Qi Zhou. 

09/27 1:50pm 
BLOC 302 
Íris Emilsdóttir Rice University 
Gap Labelling for Subshifts
JohnsonSchwartzman theorems are fundamental in gap labelling, providing sets that contain all possible spectral gap labels for dynamically defined operators. However, it remains unclear whether all elements in these sets correspond to actual open gaps and, if so, which sampling functions generate them. In this talk, we explore these questions for operators defined by subshifts over compact alphabets, focusing on the conditions under which spectral gaps open and their relationship to the underlying dynamics. Additionally, we will discuss the computation of the Schwartzman group for certain subshifts and its role in gap labelling. 

10/04 1:50pm 
BLOC 302 
Peter Madsen Ludwig Maximilian University of Munich 
On the asymptotic behavior at the kinetic time of a weakly interacting Fermi gas
Describing the longtime dynamical behaviour of fermionic systems is a longstanding open problem. When the coupling constant $\lambda$ of the interaction is small, the dynamics of the system up to kinetic time $t \sim \lambda^{2}$ is conjectured to be effectively governed by the BoltzmannNordheim kinetic equation. Considering a system of fermions on a cubic lattice at thermal equilibrium, we prove that the twopoint time correlation function of the manybody quantum dynamics can be computed effectively using the collisional frequency of the BoltzmannNordheim collision operator. 

10/18 1:50pm 
BLOC 302 
Christof Sparber University of Illinois Chicago 
Ground state (in)stability and longtime behavior in multidimensional Schrödinger equations
We consider Schrödinger equations with competing nonlinearities in spatial dimensions up to three, for which global existence holds (i.e. for which no finite time blowup occurs). A typical example is the case of the (focusing defocusing) cubicquintic nonlinear Schrödinger equation. We recall the notions of energy minimizing and of action minimizing ground states and show that, in general, they are nonequivalent. The question of longtime behavior of solutions, in particular the problem of groundstate (in)stability will be discussed using analytical results and numerical simulations. This is joint work with R. Carles and C. Klein. 

10/25 1:50pm 
BLOC 302 
YiSheng Lim Texas A&M University 
An operator approach to highcontrast homogenization
Homogenization refers to the approximation of PDEs with rapidly oscillating coefficients with a nice (constant coefficient) PDE. Physically, we can think of a composite that is obtained by finely mixing together a "soft" and a "stiff" material. Mathematically, we can study the PDE $div( a(x/\epsilon) grad u^\epsilon ) + u^\epsilon = f$, where the coefficient matrix is $a(y)$ is 1periodic, takes values $c_{soft} I$ at the "soft" regions, and $c_{stiff} I$ at the "stiff" regions. We want to take \epsilon to 0.
This talk focuses on the "high contrast" case $c_{soft} = \epsilon^2$ and $c_{stiff} = 1$. In other words, there is a loss of uniform ellipticity in \epsilon, and this poses fundamental mathematical challenges. To tackle this setting, I will explain the main ideas behind the operator theoretic framework developed by Cherednichenko, Ershova, and Kiselev (2020). The key object is that of a "boundary triple" in the sense of Ryzhov (2009). We obtain an effective limiting description with an $O(\epsilon^2)$ error in the operatornorm. 

11/01 1:50pm 
BLOC 302 
Christoph Fischbacher Baylor University 
TBA
TBA 

11/15 1:50pm 
BLOC 302 
Iulia Cristian University of Bonn 
Coagulation equations describing rain and sedimentation
Coagulation equations describe the evolution in time of a system of particles that are characterized by their volume. Multidimensional coagulation equations have been used in recent years in order to include information about the system of particles which cannot be otherwise incorporated. Depending on the model, we can describe the evolution of the shape, chemical composition or position in space of clusters.
In this talk, we focus on a model that is inhomogeneous in space and contains a transport term in the spatial variable modeling the sedimentation of clusters. We prove local existence of massconserving solutions for a class of coagulation rates for which in the space homogeneous case instantaneous loss of mass occurs.
This is based on a joint work with B. Niethammer and J J. L. Velázquez. 