# Events for 04/12/2024 from all calendars

## Mathematical Physics and Harmonic Analysis Seminar

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

**Location: ** BLOC 302

**Speaker: **Wei Li, DePaul University

**Title: ***Edge States on Sharply Joined Photonic Crystals*

**Abstract: **Edge states are important in transmitting information and transporting
energy. We investigate edge states in continuous models of photonic
crystals with piecewise constant coefficients, which are more
realistic and controllable for manufacturing optical devices. First,
we show the existence of Dirac points on honeycomb structures with
suitable symmetries. Then we show that when perturbed in two
appropriate ways, the perturbed honeycomb structures have a common
band gap, and when joined along suitable interfaces, there exist edge
states which propagate along the interfaces and exponentially decay
away from the interfaces. The main tools used are layer potentials,
asymptotic analysis, the Gohberg-Sigal theory and Lyapunov-Schmidt
reductions.

This is joint work with Junshan Lin, Jiayu Qiu, Hai Zhang.

## Geometry Seminar

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

**Location: ** BLOC 302

**Speaker: **Brandon Ashley, Southern Oregon University

**Title: ***A Group-Theoretic Approach to Darboux Integrable $f$-Gordon Equations*

**Abstract: **Classically, a partial differential equation is said to be Darboux integrable if its general solution can be found by only solving a system of ordinary differential equations. In this talk, we describe a transformation group-theoretic approach to the study of Darboux integrable equations and highlight how this approach can be used to solve the equivalence problem for so-called $f$-Gordon equations of the form $u_{xy} = f(x,y,u,u_x,u_y)$.