
Date Time 
Location  Speaker 
Title – click for abstract 

09/02 1:50pm 
BLOC 306 
Goong Chen Texas A&M University 
Modes of Motion of a Coronavirus and Their Interpretations in the Invasion Process into a Healthy Cell
The motion of a coronavirus is highly dependent on its modes
of vibration. If we model a coronavirus based on a elastodynamic PDEs,
then the wiggling motion of the spikes and breathing motion of the
capsid can be captured, for example.
Here, we give a quick review of this model and the associated modal
analysis through finite element computations. We then begin to study the
invasion process by a coronavirus into a healthy cell, which takes place
after the virus attacked the cell and its membrane began to fuse with
the membrane of the cell. The fusion causes an initial opening with
diameter of about 1 nm on the cell's membrane. For the invasion process
to be successful, the virus must further widen the diameter to about
100nm in order for the viral genome material to enter the healthy cell
to replicate. Can we model and simulate such a process by using a
coupled viruscell elastodynamic system? We will present our most recent
partial findings for this question through the showing of supercomputer
simulation animations. 

09/09 1:50pm 
Zoom 
Konstantin Merz Technische Universität Braunschweig 
Random Schrödinger operators with complex decaying potentials
Estimating the location and accumulation rate of eigenvalues of
Schrödinger operators is a classical problem in spectral theory and
mathematical physics. The pioneering work of R. Frank (Bull. Lond.
Math. Soc., 2011) illustrated the power of Fourier analytic methods —
like the uniform Sobolev inequality by Kenig, Ruiz, and Sogge, or the
Stein–Tomas restriction theorem — in this quest, when the potential
is nonreal and has “short range”.
Recently S. Bögli and J.C. Cuenin (arXiv:2109.06135) showed that
Frank’s “shortrange” condition is in fact optimal, thereby disproving
a conjecture by A. Laptev and O. Safronov (Comm. Math. Phys., 2009)
concerning KellerLiebThirringtype estimates for eigenvalues of
Schrödinger operators with complex potentials.
In this talk, we estimate complex eigenvalues of continuum random
Schrödinger operators of Anderson type. Our analysis relies on methods
of J. Bourgain (Discrete Contin. Dyn. Syst., 2002, Lecture Notes in
Math., 2003) related to almost sure scattering for random lattice
Schrödinger operators, and allows us to consider potentials which
decay almost twice as slowly as in the deterministic case.
The talk is based on joint work with JeanClaude Cuenin. 

09/23 1:50pm 
Bloc 306 
Alain Bensoussan University of Texas at Dallas 
Control On Hilbert Spaces and Mean Field Control
In this work, we describe an alternative approach to the general theory of Mean Field Control as presented in the book of P. Cardaliaguet, F. Delarue, JM Lasry, PL Lions: The Master Equation and the Convergence Problem in Mean Field Games, Annals of Mathematical Studies, Princeton University Press, 2019. Since it uses Control Theory and not P.D.E. techniques it applies only to Mean Field Control. The general difficulty of Mean Field Control is that the state of the dynamic system is a probability. Therefore, the natural functional space for the state is the Wasserstein metric space. P.L. Lions has suggested to use the correspondence between probability measures and random variables, so that the Wasserstein metric space is replaced with the Hilbert space of square integrable random variables. This idea is called the lifting approach. Unfortunately, this brilliant idea meets some difficulties, which prevents to use it as an alternative, except in particular cases. In using a different Hilbert space, we study a Control problem with state in a Hilbert space, which solves the original Mean Field Control problem, as a particular case, and thus provides a complete alternative to the approach of Cardaliaguet, Delarue, Lasry, Lions. Based on Joint work with P. J. GRABER, P. YAM.
Research supported by NSF grants DMS 1905449 and 2204795. 

09/30 1:50pm 
BLOC 306 
Jie Xiao Memorial University 
Geometric relative capacity
Principally inspired by the very geometrically physic characteristics of the divergence theorem (regarded as one of the fundamental theorems within mathematical physics & vector calculus), this talk will address: quasilinear relative capacity; deficits via isocapacity & isoperimeter; geometric Green/Robin function; trace principle & energy evaluation; quasilinear graph mass & mean curvature. 

10/07 1:50pm 
BLOC 306 
Rodrigo Matos TAMU 
Eigenvalue statistics for the disordered Hubbard model within HartreeFock theory
Localization in the Hubbard model within HartreeFock theory was previously established in joint work with J. Schenker, in the regime of large disorder in arbitrary dimension and at any disorder strength in dimension one, provided the interaction strength is sufficiently small.
I will present recent progress on the spectral statistics conjecture for this model. Under weak interactions and for energies in the localization regime which are also Lebesgue points of the density of states, it is shown that a suitable local eigenvalue process converges in distribution to a Poisson process with intensity given by the density of states times Lebesgue measure. If time allows, proof ideas and further research directions will be discussed, including a Minami estimate and its applications. 

10/28 1:50pm 
BLOC 306 
Matthias Hofmann TAMU 
Spectral minimal partitions of unbounded metric graphs
We investigate the existence or nonexistence of spectral minimal partitions of unbounded metric graphs, where the operator applied to each of the partition elements is a Schrödinger operator of the form $\Delta + V$ with suitable (electric) potential $V$, which is taken as a fixed, underlying ``landscape'' on the whole graph.
We show that there is a strong link between spectral minimal partitions and infimal partition energies on the one hand, and the infimum $\lambda_{\text{ess}}$ of the essential spectrum of the corresponding Schrödinger operator on the whole graph on the other, which recalls a similar principle for the eigenvalues of the latter: for any $k\in\mathbb N$, the infimal energy among all admissible $k$partitions is bounded from above by $\lambda_{\text{ess}}$, and if it is strictly below $\lambda_{\text{ess}}$, then a spectral minimal $k$partition exists. We illustrate our results with several examples of existence and nonexistence of minimal partitions of unbounded and infinite graphs, with and without potentials.
The nature of the proofs, a key ingredient of which is a version of Persson's theorem for quantum graphs, strongly suggests that corresponding results should hold for Schrödinger operatorbased partitions of unbounded domains in Euclidean space.
Joint project with James Kennedy and Andrea Serio. 

11/11 1:50pm 
BLOC 306 
Gamal Mograby Tufts University 


11/18 09:00am 
ZOOM 
Alexey Kostenko University of Lubljana 
TBA 

11/18 1:50pm 
BLOC 306 
Jorge Villalobos LSU 


12/02 1:50pm 
BLOC 306 
Tal Malinovitch Yale University 
