Sep

28

Tue

Title: Introduction to Modal Logic: Filtrations and Finite Model Property of $S_5$

Abstract : We’ll introduce some basic notions from Modal Logic namely, Kripke Frames, Standard Models, Filtrations etc. Then we’ll demonstrate the Finite Model Property of the system $S_5$ and this will be our main goal.

Oct

26

Tue

Speaker: B. Kjos-Hanssen

Title: Refuting a generalization of Frankl’s conjecture for lattice-like posets

Nov

23

Tue

Janitha Awedige will discuss the paper

“Inference Rules for Probability Logic” by Marija Boricic.

Feb

24

Thu

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.

## University of Hawaiʻi at Mānoa