Events
Department of Mathematics and Statistics
Texas Tech University
We study the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but coherent way. We prove that every decaying solution admits an asymptotic expansion of a new type. This expansion contains a new variable that allows it to be established in a closed-form, but does not affect the meaning and precision of the expansion. Moreover, the expansion is constructed explicitly with the use of the complexification method.
I will report on joint work with Samuel Pérez-Ayala. We derive a sharp upper bound for the first eigenvalue $\lambda_{1,p}$ of the $p$-Laplacian on asymptotically hyperbolic manifolds for $p$ larger than $1$. We then prove that a particular class of conformally compact submanifolds within asymptotically hyperbolic manifolds are themselves asymptotically hyperbolic. As a corollary, we show that for any minimal conformally compact submanifold $Y^{k+1}$ within $\mathbb{H}^{n+1}(-1)$, $\lambda_{1,p}(Y)=\left(\frac{k}{p}\right)^{p}$. We then obtain lower bounds on the first eigenvalue of these submanifolds in the case where minimality is replaced with a weaker mean curvature assumption and where the ambient space is a general Poincaré-Einstein space whose boundary is of non-negative Yamabe type. In the process, we introduce an invariant $\hat{\beta^Y}$ for each such submanifold, enabling us to generalize a result due to Cheung-Leung.
 | Wednesday
Jan. 29
12 PM
online
|
| Quantum Homotopy
Vector fields
Dmitri Pavlov
Department of Mathematics and Statistics, Texas Tech University
|
A very brief introduction to differential forms, Cartan calculus, Lie groups and Lie algebras.The aim of the talk is to give a nice visual introduction to the world of knot theory. This talk provides the foundation of a new cryptographic protocol, involving knots. This is joint work with Silvia Sconza.
Join the Zoom Meeting at 3 PM (CST UT-6)
Meeting ID: 958 5298 7437
Passcode: 922447
Abstract PDF
This presentation may be viewed in the TTU Mediasite catalog via eraider login.
abstract 2 PM CST (UT-6)
Zoom link available from Dr. Brent Lindquist upon request.