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).