My Past Life

When I was an undergraduate, I was mostly interested in pure mathematics, especially algebraic geometry and later probability. I ran the Columbia Undergraduate Math Society (UMS) from the Autumn of 2016 to the Spring of 2019, where I organized a number of talks aimed at advanced undergraduates. During the summers, I organized a reading group and would organize the speakers and general curriculum. In the summer of 2018, we studied Representation Theory of the Symmetric Group, while in 2017 we read about Elliptic Curves.

I was also a student (2014) and then counselor (2017, 2018, 2019) at the wonderful PROMYS program, which helps advanced high school students learn rigorous, proof-based number theory. During this time, I gave a number of talks, both to the students, and to the other counselors (who are also undergraduates). In my last year, I designed a six-part series on probability and stochastic processes to teach the other college students, complete with problem sets and solutions. Notes for these talks are below, separated by their intended audience.

Below are some expository notes related to talks I gave in the above contexts or final projects in various classes.

For Undergraduates and above

1. Intersections of Smooth Varieties. Part of the Graduate Seminar in Intersection Theory in Algebraic Geometry, Fall 2018.

2. Probability and Stochastic Processes. A 6-part series with problem sets given at PROMYS 2019.

3. Reperesentation Theory of the Symmetric Group. A 3-part series given with Roger Van Peski at PROMYS 2018.

4. Introduction to the Representation Theory of Finite Groups. A quick introduction to my representation theory series above, given at PROMYS 2018.

5. Symmetric Unimodal Sequences. A 2-part series on applying representation theory to combinatorics given at PROMYS 2017.

6. Intersections of Nonsingular Varieties. A 3-part series on intersection theory at PROMYS 2017.

7. The Riemann-Hurwitz Theorem and Applications. Part of a series on classical algebraic geometry at PROMYS 2017.

8. Introduction to Artin L-Functions. Final project for a course on Class Field Theory taught by Chao Li.

9. The Riemann-Roch Theorem. Final project for a course on algebraic geometry taught by Johann Dejong.

10. Elliptic Curves. Final project for a course on algebraic number theory taught by Chao Li.

For High School Students

1. Fermat's Last Theorem for Polynomials.

2. Monsky's Theorem

3. The Skolem-Mahler-Lech Theorem