### Mentoring

**Undergraduate Research Opportunities Program (UROP)**

- (Summer 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.

**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)**

- (Spring 2024 – Summer 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 hope to give unified approach with some interesting applications and some new results. Richie was awarded $1,500 by the Utah Math Department for his work on this project. Richie gave a talk about this project at Math For All SLC in April 2024.
- (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 double funded for this project for the 2023 summer semester! He was awarded
- $1,125 by the Utah Math Department and
- $875 by the current NSF Research Training Group at Utah:
*RTG: Algebra, Geometry, and Topology at the University of Utah*

**Introduction to Research Projects (Utah)**

- (Summer 2023) Worked with two of my former students on a funded 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.

**Other projects and mentoring**

- (Summer 2024) Worked with two undergraduate math majors, Izzy Zahalak and Abby Linscott, 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.
- (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.