Events for 08/23/2023 from all calendars

P and T Talk- A Tale of Two Solitons

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Jonas Luhrmann

Description: Abstract: Solitons are particle-like solutions to nonlinear dispersive evolution equations, which model a variety of wave propagation phenomena. A basic question about the dynamics of a soliton is its asymptotic stability, in other words, how it behaves when it gets jolted a little bit. This talk is a story about the asymptotic problems for the soliton of the so-called sine-Gordon equation and for the soliton of the closely related cubic Klein-Gordon equation on the line. We will see that while these two problems are very similar at first sight, they differ by a subtle cancellation structure with drastic consequences for the analysis of the dynamics.

P and T Talk- Decomposition and duality in chromatic homotopy theory

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Irina Bobkova

Description: Abstract: Computation of the stable homotopy groups of spheres is a long-standing open problem in algebraic topology. I will introduce chromatic homotopy theory -- a powerful framework for organizing computations and describing large scale patterns in stable homotopy groups. It splits the problem into chromatic levels, and each level can be studied using the theory of formal group laws and their deformations. Levels 0 and 1 are long understood; level 2 is an area of active interest. I will describe several projects at chromatic level 2 which explore natural notions of duality and invertibility in this context.