Farzana Nasrin (University of Hawaiʻi) @ Lecture held in Elysium
Dec 1 @ 6:00 am – 8:00 am

Title: Bayesian Statistics, Topology and Machine Learning for Complex Data Analysis
by Farzana Nasrin (University of Hawaiʻi) as part of Topological Groups

Lecture held in Elysium.

Analyzing and classifying large and complex datasets are generally challenging. Topological data analysis, that builds on techniques from topology, is a natural fit for this. Persistence diagram is a powerful tool that originated in topological data analysis that allows retrieval of important topological and geometrical features latent in a dataset. Data analysis and classification involving persistence diagrams have been applied in numerous applications. In this talk, I will provide a brief introduction of topological data analysis, focusing primarily on persistence diagrams, and a Bayesian framework for inference with persistence diagrams. The goal is to provide a supervised machine learning algorithm in the space of persistence diagrams. This framework is applicable to a wide variety of datasets. I will present applications in materials science, biology, and neuroscience.

Mikhail Tkachenko (Metropolitan Autonomous University) @ Lecture held in Elysium
Dec 8 @ 6:00 am – 8:00 am

Title: Pseudocompact Paratopological and Quasitopological Groups
by Mikhail Tkachenko (Metropolitan Autonomous University) as part of Topological Groups

Lecture held in Elysium.

Pseudocompactness is an interesting topological property which acquires very specific
features when applied to different algebrotopological objects. A celebrated theorem
of Comfort and Ross published in 1966 states that the Cartesian product of an arbitrary
family of pseudocompact topological groups is pseudocompact. We present a survey
of results related to the validity or failure of the Comfort-Ross’ theorem in the realm of
semitopological and paratopological groups and give some examples showing that
pseudocompactness fails to be stable when taking products of quasitopological groups.