**Mentoring**

I really enjoy working with undergraduate students on math projects. It reconnects me with my passion for math and it is usually a lot of fun! Below are some of the unique projects I’ve been able to help organize. If you are an undergraduate who is interested in doing a reading course or research project, feel free to send me an email.

**Resources for undergraduate research**

**Undergraduate Research Opportunities Program (UROP)**

- (Summer 2024 – Fall 2024) Richie Sheng (undergraduate math major at Utah) is working on project related to the Buchweitz-Greuel-Schreyer Conjecture. This project is funded by the University of Utah’s Office of Undergraduate Research through UROP. Richie was awarded as stipend of $1,200 for his work over the summer and his project was renewed for the fall semester of 2024.

**Science Research Initiative (Utah)**

- (Spring 2024 – Fall 2024) I am working with three first year undergraduate students on a three semester long project about the mathematics of the card game SET. This project is a
*research stream*organized through the University of Utah’s Science Research Initiative (SRI is a program which gets undergraduate students involved in research in as early as their second semester).

**Independent REU Projects (Utah)**

*The projects in this category were funded by the University of Utah Math Department and, in some cases, additional funding was awarded by the NSF Research Training Group at Utah* *(RTG: Algebra, Geometry, and Topology at the University of Utah)*

- (Summer 2024) Richie Sheng and Debbie Wooton (both undergraduate math majors at Utah) worked with Trung Chau and myself on a project about resolutions of monomial ideals. More specifically, we studied when the connected and path ideals of a graph are minimally resolved by the Scarf complex. Richie and Debbie were both awarded $2,000 for their work on this project.
- (Spring 2024) Richie Sheng (undergraduate math major at Utah) and I worked on a project regarding a “d-fold” version of the tensor product of matrix factorizations. The construction has been studied in several different forms. We give a unified approach with some interesting applications and some new results. Richie was awarded $1,500 for his work on this project. Richie also gave a talk about this project at Math For All SLC in April 2024 and at the University of Utah Undergraduate Research Symposium.
- (Fall 2022 – Fall 2023) London Adams (undergraduate math/physics major at Utah) and I worked on some simple questions related to the Buchweitz-Greuel-Schreyer Conjecture. This conjecture gives a lower bound for the smallest possible matrix factorization of a given polynomial. London was awarded $2,000 for his work on this project.
- (Summer 2023) Worked with two students on a reading project on advanced topics in Linear Algebra. This project was meant to prepare them for future research. Both students were awarded a stipend for their participation in the project: Storey Peacock (math/economics major at Utah) awarded $750 by the Utah Math Dept. Sathya Tadinada (math/computer science major at Utah) awarded $750 by the Utah Math Dept.
- Storey is now pursuing a PhD in mathematics at the University of Colorado Boulder.

**Other projects and mentoring**

- (Summer 2024) Worked with two undergraduate math majors on an independent reading project. We a variety of topics in homological algebra including free resolutions of modules over commutative rings.
- (Summer 2023) Ann Bigelow (applied math major) and I spent the summer (2023) trying to more carefully understand some applications of SVD. We created some simple examples of Principal Component Analysis (PCA) which I then used as a lab in my linear algebra course in the fall of 2023.
- Ann is now pursuing a PhD in applied mathematics at the University of Wisconsin – Madison

- (Summer 2023 – Fall 2023) Worked with Richie Sheng (undergraduate math major at Utah) on a supervised reading course (called MATH 5910 at Utah) on Galois Theory.
- (Fall 2022) Haidong Zhao — now pursuing a graduate degree in Data Science at the University of British Columbia!

**Directed Reading Program (Syracuse)**

- (Spring 2022) Chance Baggett (math/physics major at Syracuse University) and I worked on a semester long directed reading as part of the Syracuse DRP.
- Chance has since been named the 2023-2024 Astronaut Scholar at Syracuse! This is a very prestigious award which includes an all expenses paid trip to Orlando for the ASF Innovators Week and Gala.