Decompositions of Modules over Subalgebras of Truncated Polynomial Rings - Joint Mathematics Meeting 2022
Abstract: We investigate how modules decompose over principal subalgebras of certain truncated polynomial rings. In particular, we will investigate how a module decomposition may (or may not) change when we decompose over different principal subalgebras. Varying decompositions are related to the notion of rank varieties. Finally, we will examine how one might extend the notion of rank varieties to more general truncated polynomial rings.
In April 2018, I gave a talk over Continued Fractions to a group of my fellow graduate students at Sam Houston State University/ This was my project with Dr. Ken Smith for my Masters' degree. The notes that I used during this lecture are included in the link above. Continued fractions have many applications, including, but not limited to computing square roots, Pell's equation, representing irrational numbers and knot theory.
Joint Mathematics Meetings 2022 - Spring 2022 - Seattle, Washington
National Association of Mathematicians MATHFest - Fall 2021 - Virtual
Free Resolutions and Representation Theory (ICERM) - Fall 2020 - Virtual
Math Summer Workshop for Achieving Greater Graduate Education Readiness (Math SWAGGER) - Summer 2020 - Virtual
Southwest Local Algebra Meeting (SLAM) - Spring 2020 - New Orleans, LA
Southwest Local Algebra Meeting (SLAM) - Spring 2019 - El Paso, TX
Gulf States Math Alliance Conference - Spring 2019 - Arlington, TX
Field of Dreams Conference - Fall 2018 - St. Louis, Missouri
Field of Dreams Conference - Fall 2017 - St. Louis, Missouri