Speaker: Chuang Xu (Technical University Munich)
Analyzing walks with combinatorics and automata theory
The enumeration theorem by Chomsky and Schützenberger revealed
a significant intersection between the theory of automata and
enumerative combinatorics. Since then, much progress has been made in
both fields. However, their intersection remains unchanged in the sense
that no further enumeration theorem emerged beyond that of
Chomsky-Schützenberger. We survey the literature in both fields and
picture what it would look like to expand the intersection between them.
Michael W. Stewart Monday 02 May 2022 3:30 pm Keller, room 302
Title: “A numerical method for solving the eigenvalue problem associated with neutron diffusion inside nuclear reactor cores”
Abstract: “In this talk we will explore a mathematical tool that might assist in tackling one problem in the design of nuclear reactors, namely a numerical method for finding solutions to the neutron diffusion equation during steady state operations. After a brief look at the physics of nuclear fission and the physical aspects of nuclear reactors we will derive a partial differential equation that can be used to model such systems in a time independent steady state. The use of finite element discretization allows us to find weak solutions to the eigenvalue problem which emerges, and so we review weak solutions, the discretization of continuous problems, and what is known about the linear systems that such discretization produces. The solutions of such a discretized problem will naturally differ from the exact solution, and so we set bounds on the errors that are introduced. A possible algorithm to solve the generalized eigenvalue problem, and some computational experiments will then be reviewed.”
Jason L Greuling Tuesday, May 3rd, 3pm Keller 302
Title: A Discrete Regge Complex
This paper is interested in a differential complex that arises in the study of finite element methods for certain partial differential equations from Riemannian geometry involving curvature. Specifically, we derive a two dimensional Regge complex that includes the linearized curvature operator, curlTcurl, and relate it to a complex that includes the linearized discrete notion of curvature on a triangulation. We establish a correspondence between the two complexes, giving a relationship between the two linearized maps.