EPaDel-NJ Fall 2023 Section Meeting

Judith Covington
Northwestern State University
Math Teachers' Circles - What, Why, When, and How?

Kristen Hendricks
Rutgers University
A First Look at Knots and Symmetries

A mathematical knot is a simple object -- take a piece of string, tie it up however you like, and glue the ends together so you can't untie it. But these deceptively easy objects to describe and fiddle with are key to understanding deep geometric questions, many not nearly so accessible. We'll introduce knots and consider some possible measures of how complicated a knot is, before turning our attention to one of my favorite topics, possible symmetries of knots. In the end, we'll see how different types of symmetry have wildly different relationships with how "complicated" the knots involved are.

Kristen Hendricks is a low-dimensional and symplectic topologist. Most of her work is focused on developing equivariant versions of various Floer-theoretic invariants and exploring their applications to problems of 3-manifolds and knots. She did her undergraduate degree in mathematics at Harvard, followed by doctoral work at Columbia and a postdoctoral position at UCLA. After three years as an assistant professor at Michigan State, she moved to Rutgers, where she is presently an associate professor. Her work has been recognized by an NSF CAREER grant (2018), a Sloan Research Fellowship (2019), and an AWM Birman Research Prize in Topology and Geometry (2023). When not doing mathematics, she enjoys science fiction novels and unnecessarily complicated knitting projects.

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Jason Rosenhouse
US Air Force Academy
James Madison University
Dirichlet's Theorem and the Rise of Analytic Number Theory

In 1837, Peter G. L. Dirichlet proved the following theorem: If a and d are relatively prime integers, then the arithmetic progression a, a+d, a+2d, ... contains infinitely many prime numbers. His proof ushered in a revolution in number theory because it relied in a critical way on complex analysis. The use of analytic methods to solve problems in number theory was a tremendous innovation at the time. We shall consider some of the details of Dirichlet's proof, focusing on understanding why there is a deep connection between these seemingly unrelated branches of mathematics.

Jason Rosenhouse is a professor of mathematics at James Madison University, Harrisonburg, VA. For the 2023-2024 academic year, he is the Distinguished Visiting Professor in the Department of Mathematical Sciences at the U. S. Air Force Academy, Colorado Springs, CO. He received his PhD in mathematics from Dartmouth College, Hanover, NH in 2000, specializing in number theory and combinatorics. He is the author or editor of nine books on topics such as recreational mathematics and evolution vs. creationism. Currently, he is the editor of Mathematics Magazine, published by the MAA. When not doing math, he enjoys chess, cooking, and reading locked-room mysteries.

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