Dear Colleagues,

You are most cordially invited to the seminar organized by the Department of Mathematics.

Title: A Discussion of Invisibility, Nonlinearity and the Existence of Blow up Solutions in Scattering Theory

Speaker: Neslihan Oflaz (Koç Technology)

Abstract: Scattering theory is a framework of considerable experimental and theoretical interest that describes the interaction/scattering of waves and particles. There is a wide range of scattering processes that are studied under different branches of physics, such as the collision of particles in classical physics, scattering of electromagnetic waves through a medium in electromagnetism, scattering of low energy quantum particles in quantum mechanics, or creation/annihilation of particles in high energy particle physics. In this talk, I will discuss the scattering processes modeled by linear and nonlinear time independent Schrödinger equations. First, I will review the concepts such as Jost solutions, transfer matrices, unidirectional reflection and invisibility. In particular, I will represent some theorems regarding the properties of transfer matrices for the linear case and argue the validity of these theorems in the presence of nonlinearity in Schrödinger equations. Also, I will examine the conditions for the existence of blow up solutions for such systems.

Date: Wednesday, December 23, 2020

Time: 17:00

Google Meet:

Please find the abstract attached.