Xingyu Cheng

Quick links:

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 roughly interested in algebraic geometry and representation theory. I think a lot about moduli of vector bundles on curves and local systems.

Email:

xcheng1 (at) unc (dot) edu

Some miscellaneous notes

Zariski's Main Theorem. This is a set of notes I wrote for a class presentation on Zariski's Main Theorem.

Module of Differentials. This is a set of notes for a class presentation on module of differentials.

Semigroup Theory. This is a set of notes for a final class project on semigroup theory in PDEs.

Dynkin Diagrams. A set of notes for a final project about Dynkin Diagrams and root systems.

What's in a scheme? A set of notes for a talk I gave at jGMRT, a weekly student ran seminar about topics in geometric representation theory.

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.