Apr

5

Tue

Speaker: Chuang Xu (Technical University Munich)

Apr

7

Thu

Title:

Analyzing walks with combinatorics and automata theory

Abstract:

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.

May

2

Mon

**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.”

May

3

Tue

**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.

## University of Hawaiʻi at Mānoa