Mathematical Physics and Harmonic Analysis Seminar

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 Central ll
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 
TBA 
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 
TBA 
Alain Bensoussan University of Texas at Dallas 
TBA 

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. 

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


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

The organizers for this seminar are
Bob Booth
and
Rodrigo Matos.
Email them with talk suggestions and to request the Zoom link.