# Events for 09/02/2022 from all calendars

## Student/Postdoc Working Geometry Seminar

**Time: ** 1:30PM - 2:30PM

**Location: ** BLOC 628

**Speaker: **Runshi Geng, TAMU

**Title: ***Intersections of unitary groups arising in quantum information theory*

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** BLOC 306

**Speaker: **Goong Chen, Texas A&M University

**Title: ***Modes of Motion of a Coronavirus and Their Interpretations in the Invasion Process into a Healthy Cell*

**Abstract: **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 virus-cell elastodynamic system? We will present our most recent
partial findings for this question through the showing of supercomputer
simulation animations.

## Promotion Talk by Igor Zelenko

**Time: ** 4:00PM - 5:00PM

**Location: ** Bloc 117

**Description: **Title: Projective and affine equivalence of sub-Riemannian metrics

Abstract: Sub-Riemannian metrics on a manifold are defined by a distribution (a
subbundle of the tangent bundle) together with a Euclidean structure on
each fiber. The Riemannian metrics correspond to the case when the
distribution is the whole tangent bundle. Two sub-Riemannian metrics are
called projectively equivalent if they have the same geodesics up to a
reparameterization and affinely equivalent if they have the same
geodesics up to affine reparameterization. In the Riemannian case, both
equivalence problems are classical: local classifications of
projectively and affinely equivalent Riemannian metrics were established
by Levi-Civita in 1898 and Eisenhart in 1923, respectively. In
particular, a Riemannian metric admitting a nontrivial (i.e.
non-constant proportional) affinely equivalent metric must be a product
of two Riemannian metrics i.e. separation of variables (the de Rham
decomposition) occur, while for the analogous property in the
projective equivalence case a more involved ("twisted") product
structure is necessary. The latter is also related to the existence of
commuting nontrivial integrals quadratic with respect to velocities for
the corresponding geodesic flow. We will describe the recent progress
toward the generalization of these classical results to sub-Riemannian
metrics. The talk is based on joint works with Frederic Jean, Sofya
Maslovskaya (my former Ph.D. student), Zaifeng Lin (my current Ph.D.
student), and Andrew Castillo (my former Master's student).