David Webb: Kripke semantics for the provability logic GL
Nov 9 @ 10:30 am – 11:30 am
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.

Number Theory Seminar (Kedlaya) @ Keller 301
Feb 24 @ 3:00 pm – 3:45 pm
The relative class number one problem for function fields

Abstract: Gauss conjectured that there are nine imaginary quadratic fields of class number 1; this was resolved in the 20th century by work of Baker, Heegner, and Stark. In between, Artin had introduced the analogy between number fields and function fields, the latter being finite extensions of the field of rational functions over a finite field. In this realm, the class number 1 problem admits multiple analogues; we recall some of these, one of which was “resolved” in 1975 and then falsified (and corrected) in 2014, and another one of which is a brand-new theorem in which computer calculations (in SageMath and Magma) play a pivotal role.


Number Theory Seminar (Bucur) @ Keller 301
Feb 24 @ 4:15 pm – 5:00 pm
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