Speaker: B. Kjos-Hanssen
Title: Refuting a generalization of Frankl’s conjecture for lattice-like posets
Janitha Awedige will discuss the paper
“Inference Rules for Probability Logic” by Marija Boricic.
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.
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.