Logic seminar: Janitha Aswedige
Nov 23 @ 10:30 am – 11:30 am

Janitha Awedige will discuss the paper
“Inference Rules for Probability Logic” by Marija Boricic.

Oleksandr Markovichenko’s thesis presentation on: Persistent cohomology of cover refinements
Mar 10 @ 3:00 pm – 4:00 pm

Topological data analysis (TDA) is a new approach to analyzing complexdata which often helps reveal otherwise hidden patterns by highlightingvarious geometrical and topological features of the data. Persistenthomology is a key in the TDA toolbox. It measures topological featuresof data that persist across multiple scales and thus are robust withrespect to noise. Persistent homology has had many successfulapplications, but there is room for improvement. For large datasets,computation of persistent homology often takes a significant amount oftime. Several approaches have been proposed to try to remedy this issue,such as witness complexes, but those approaches present their owndifficulties.

In this work, we show that one can leverage a well-known data structurein computer science called a cover tree. It allows us to create a newconstruction that avoids difficulties of witness complex and canpotentially provide a significant computational speed up. Moreover, weprove that the persistence diagrams obtained using our novelconstruction are actually close in a certain rigorously defined way topersistent diagrams which we can get using the standard approach basedon Čech complexes. This quantifiable coarse computation of persistentdiagrams has the potential to be used in many applications wherefeatures with a low persistence are known to be less important.

Colloquium- Chuang Xu (Technical University Munich)
Apr 5 @ 3:30 pm – 4:30 pm

Speaker: Chuang Xu (Technical University Munich)

Logic seminar: Jack Yoon
Apr 7 @ 3:00 pm – 4:00 pm

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.

Colloquium: Lutz Strüngmann (Mannheim University) @ Keller 302
Apr 22 @ 3:30 pm – 4:30 pm
Ryan Sasaki MA presentation
Apr 28 all-day
Stewart’s MA presentation
May 2 @ 3:30 pm – 4:00 pm

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.”

Greuling’s MA presentation
May 3 @ 3:00 pm – 4:00 pm

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.