Colloquia, Autumn 2022
Tom Britton (University of Stockholm)
Title: Mathematical models for epidemics (including Covid-19)
In the talk I will first describe the basics for mathematical epidemic models, and indicate the many extensions that exist. Then I will briefly describe three problems I (and many others) have worked on during Covid-19: Herd immunity, Optimizing interventions in time and magnitude, and Estimating the effects of various behaviour changes during the epidemic.
Gustaf Söderlind (University of Lund)
Title: Logarithmic norms and Quadratic forms
The logarithmic norm was introduced in 1958 for matrices, for the purpose of estimating growth rates in initial value problems. Since then, the concept has been extended to spectral theory, nonlinear maps, differential operators and function spaces. There are applications to operator equations in general, including evolution equations as well as boundary value problems and PDEs. A broad introduction to the topic will be given, demonstrating the recurring pattern found in various applications.
Jan Philip Solovej (University of Copenhagen)
Title: The dilute limit of quantum gases
I will introduce the mathematics of quantum many-body problems. In particular, I will discuss systems of many interacting particles that obey either Bose or Fermi statistics. I will discuss the notion of the thermodynamic limit, where the size of the system tends to infinity while the particle density is fixed. The quantity of main interest is the ground state energy density (energy per volume) as a function of particle density. I will review some results in the limits of large and small particle density in 1, 2, and 3 dimensions. The main focus will be on small density, i.e., the dilute limit. This has been an area of very active research in the past few years and an old conjecture from the 1950s relating the issue to the theory of superfluidity has been resolved. There are however still many open problems.
Gustavo Jasso (University of Lund)
Title: Brackets, trees and the Borromean rings
I will describe some of the combinatorics that emerge from the familar associativity equation
(ab)c = a(bc),
and explain how these encode fundamental algebraic structures that are now ubiquitous in Algebra, Geometry and Topology.
Fredrik Kahl (Chalmers University of Technology)
Title: Deep Learning for Geometry and Geometry for Deep Learning