Eddy Kwessi, Trinity University
Visit Computational Analysis Seminar page for Zoom meeting information

Lillian Pierce, Duke University
Email Math Colloquium to request Zoom ID and pass code

Many questions in number theory can be phrased as counting problems. How many number fields are there? How many elliptic curves are there? How many integral solutions to this system of Diophantine equations are there? If the answer is “infinitely many,” we want to understand the order of growth for the number of objects we are counting in the “family.” But in many settings we are also interested in finer-grained questions, like: how many number fields are there, with fixed degree and fixed discriminant? We know the answer is “finitely many,” but it would have important consequences if we could show the answer is always “very few indeed.” In this accessible talk, we will describe a way that these finer-grained questions can be related to the bigger infinite-family questions. Then we will use this perspective to survey interconnections between several big open conjectures in number theory, related in particular to class groups and number fields. (Contact Person: Larry Rolen)

Annalaura Stingo, University of California Davis
Visit PDE Seminar page for Zoom meeting information

Taufiquar Khan, University of North Carolina at Charlotte
Visit Computational Analysis Seminar page for Zoom meeting information

Karen Vogtmann, University of Warwick
Email Math Colloquium to request Zoom Meeting ID and passcode

Jason Metcalfe, University of North Carolina at Chapel Hill
Visit PDE Seminar page for Zoom meeting information

Yu-Min Chung, University of North Carolina at Greensboro
Visit Computational Analysis Seminar page for Zoom meeting information

Topological data analysis (TDA) is a rising field at the intersection of Mathematics, Statistics, and Machine Learning. Techniques from this field have proven successful in analyzing a variety of scientific problems and datasets. The main driving force in TDA is the development of persistent homology, which studies the intrinsic shape of data. Persistent homology is a mathematical construction from the field of algebraic topology, and in practice, persistence diagrams (summaries of the persistent homology) yield topological information. However, the space of persistence diagrams is notoriously difficult to work with (for instance, the mean of persistence diagrams may not be unique). Transforming persistence diagrams into vectors or functions while preserving their critical information is one of the major research areas in TDA. In this talk, we will give a brief introduction to persistent homology, and we will demonstrate methods we propose to summarize persistence diagrams. Applications to various datasets from cell biology, medical imaging, physiology, and climatology, will be presented to illustrate the methods. This talk is designed for a general audience in mathematics. No prior knowledge in algebraic topology is required.

Stephen Taylor, New Jersey Institute of Technology
Visit PDE Seminar page for Zoom meeting information

Stefan Czimek, Brown University
Visit PDE Seminar page for Zoom meeting information

Penghang Yin, University at Albany
Visit Computational Analysis Seminar page for Zoom meeting information