Xingyu Cheng

Quick links:

• CV
• JGMRT
• Some miscellaneous notes
• Github

Hi there!

My name is Xingyu (Tiger) Cheng. I am a 3rd year mathematics PhD student at UNC Chapel Hill working under Prakash Belkale. I received my undergraduate degree at Purdue University in 2021 with a BS in mathematics and with minors in German and Computer Science. I am interested in vector bundles over curves and associated enumerative problems. In a past life I also played viola at the Purdue orchestras.

I am on currently on the job market.

Email:

xcheng1 (at) unc (dot) edu

Research

1. (In preparation, pdf available upon request) Stability of parabolic systems of Hodge bundles over punctured \(\mathbb P^1\)
2. Linking number of monotonic cycles in random book embeddings of complete graphs joint with Yasmin Aguillon, Eric Burkholder, Spencer Eddins, Emma Harrell, Kenji Kozai, Elijah Leake, Pedro Morales (2023)
3. The Mean Sum of Squared Linking Numbers of Random Piecewise-Linear Embeddings of \(K_n\) joint with Yasmin Aguillon, Spencer Eddins, Pedro Morales (2023)

Mentoring

At UNC I've had the opportunity to be a graduate student mentor for the Directed Reading Program (DRP):

The Directed Reading Program (DRP) pairs undergraduate students with graduate student mentors for semester-long independent study projects. It is an opportunity for motivated students to get one-on-one mentorship as they learn about a math topic of their interest but is out of the scope of the courses offered at UNC. Topics can include specific problems of interest, more in-depth learning about a course topic, or an introduction to higher level math.

• Fall 2022: I mentored Marleigh Purgar-Mcdonald on the basics of algebraic geometry and commutative algebra. We followed roughly the treatment given in Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea.
• Spring 2023: I mentored Aryan Kokkanti on the basics of topology and knot theory. We followed some of the contents Colin Adams' The Knot Book.
• Fall 2023: I mentored Paul Hamrick on algebraic geometry by going through Miles Reid's Undergraduate Algebraic Geometry. Our main goal for the semseter was to understand the proof of 27 lines.
• Spring 2024: I mentored Yan Zhu on number theory and basic abstract algebra. We followed roughly some of Ireland and Rosen as well as relevant parts of Dummit and Foote.
• Spring 2025: I mentored Yuxin Ge on the basics of field and Galois theory from some sections of Milne's notes. In particular, we focused on understanding fields and field automorphisms.
• Fall 2025: I will be mentoring Vanessa Almelor this semester. We plan on going through Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea.