Decompositions of Modules over Subalgebras of Truncated Polynomial Rings - Joint Mathematics Meeting 2022 (Postponed)
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 November 2021, I had the pleasure of presenting a poster at the Blackwell-Tapia conference held at MSRI. The poster gives a brief introduction into my research area. You can access the pdf file by clicking the link above. First, we look at some examples of how modules decompose over principal subalgebras of certain truncated polynomial rings. In particular, we investigate how the decompositions for these modules can change (or not) due to our choice of our principal subalgebra. Then, we introduce the definition of a rank variety in terms of these particular modules. Finally, we investigate how the rank variety of a module relates to its decomposition. Let me know if you'd like to hear more!
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. My notes 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 (Postponed)
Blackwell-Tapia Conference - Fall 2021 - Berkeley, CA (MSRI)
Graduate Algebra Symposium - Fall 2021 - Virtual
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