The APDE seminar on Monday, 2/22, will be given by Alexis Drouot online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis () or Federico Pasqualotto ().

Title: Mathematical aspects of topological insulators.

Abstract: Topological insulators are intriguing materials that block conduction in their interior (the bulk) but support robust asymmetric currents along their edges. I will discuss their analytic, geometric and topological aspects using an adiabatic framework favorable to quantitative predictions.

The APDE seminar on Monday, 2/8, will be given by Kihyun Kim online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis () or Federico Pasqualotto ().

Title: Blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation

Abstract: We consider the blow-up dynamics for the self-dual Chern-Simons-Schrödinger equation (CSS) under equivariance symmetry. (CSS) is $L^2$-critical, has the pseudoconformal symmetry, and admits a soliton $Q$ for each equivariance index $m \geq 0$. An application of the pseudoconformal transformation to $Q$ yields an explicit finite-time blow-up solution $S(t)$ which contracts at the pseudoconformal rate $|t|$. In the high equivariance case $m \geq 1$, the pseudoconformal blow-up for smooth finite energy solutions in fact occurs in a codimension one sense, but also exhibits an instability mechanism. In the radial case $m=0$, however, $S(t)$ is no longer a finite energy blow-up solution. Interestingly enough, there are smooth finite energy blow-up solutions whose blow-up rates differ from the pseudoconformal rate by a power of logarithm. We will explore these interesting blow-up dynamics (with more focus on the latter) via modulation analysis. This talk is based on my joint works with Soonsik Kwon and Sung-Jin Oh.