Andrew Lin

Research

• Supposedly as a grad student this is something I'm supposed to be doing now? Working on it...

• A curiously slowly mixing Markov chain (with Persi Diaconis and Arun Ram) studies a particularly simple instance of the Burnside process, which is a Markov chain which allows one to sample uniformly from the orbits of a group action. The Burnside process has useful applications (for example for sampling large uniform partitions or contingency tables), but proving convergence to stationarity has been very difficult in almost all cases. We find that this particular chain can be explicitly diagonalized using some very nice combinatorial and algebraic arguments, and in particular we show that the mixing time looks very different when measured in l^1 (total variation) versus l^2 (chi-square) distance to stationarity.

• High-dimensional permutons: theory and applications (with Jacopo Borga) generalizes the notion of permuton convergence to higher-dimensional permutations, while providing the first examples of some (universal) permuton limits coming from natural combinatorial structures. It has some nice pictures and interesting constructions, and there's definitely more that can be done!

• In Summer 2021, I participated in the Caltech SURF program under the mentorship of Professor Leonard Schulman. Here's the final report that I produced.

• In Summer 2020, I participated in the Texas A&M Probability and Algebra REU; here are the presentation slides and final report that I produced. You can also read the paper from our group here!

Contest math problems

I've written a few problems for the HMMT competition; here are a few that I particularly like. (All of the past problems and solutions can be found on the HMMT site.)

• HMMT February 2019 G8: In triangle ABC with AB < AC, let H be the orthocenter and O be the circumcenter. Given that the midpoint of OH lies on BC, BC=1, and the perimeter of ABC is 6, find the area of ABC.

• HMMT February 2020 C3: Each unit square of a square grid is colored either red, green, or blue. Over all possible colorings of the grid, what is the maximum possible number of L-trominos that contain exactly one square of each color? (L-trominos are made up of three unit squares sharing a corner.)

• HMMO 2020 T5: The classrooms at MIT are each identified with a positive integer (with no leading zeroes). One day, as President Reif walks down the Infinite Corridor, he notices that a digit zero on a room sign has fallen off. Let N be the original number of the room, and let M be the room number as shown on the sign. The smallest interval containing all possible values of M/N can be expressed as [a/b, c/d) where a,b,c,d are positive integers with gcd(a,b) = gcd(c,d) = 1. Compute 1000a + 100b + 10c + d.

Teaching

I was most recently a Teaching Assistant for Math 61CM (Modern Mathematics: Continuous Methods), primarily teaching the "introduction to proofs" sections. Previously, I was a Teaching Assistant for Math 21 (Calculus) in Autumn 2024, Winter 2024, and Autumn 2023, and a Course Assistant for Math 20 (Calculus) in Autumn 2022 and Math 108 (Introduction to Combinatorics and Its Applications) in Spring 2025. I also taught a section of SOAR Mathematics / Summer Bridge Mathematics (a precalculus readiness crash course for incoming first-years) in the summers of 2023, 2024, and 2025.

During the 2024-2025 academic year, I was a CTL LIT fellow, working with Alexandra Stavrianidi to run quarterly TA discussion workshops and develop a department teaching handbook. I am also coordinating the TA mentorship program in the department; if you're teaching or want to chat about your philosophies or ideas, please don't hesitate to reach out! I will almost certainly have thoughts and want to hear your thoughts too.

At MIT, I was an Undergraduate Assistant for 18.100B (Real Analysis), as well as a Teaching Assistant for 18.600 (Probability and Random Variables) for two semesters. Those were some of my academic highlights during my time as an undergrad, and I'm happy to talk about my experiences TAing! I also did some other assorted teaching (because it's always fun and rewarding to get better at explaining things):

• I was one of the lecturers for 18.S097, an undergrad-led proof-writing workshop, during IAP 2021. Here are the lecture notes that I produced for the last two lectures of the class.
• I was a JC at Canada/USA Mathcamp in Summer 2019 and taught two short classes based on material I had learned a few months ago in 18.212: an evening talk on the matrix-tree theorem, as well as a Week 5 class cotaught with Shiyue Li on a proof of the hook-length formula.

Music

• The MIT Video Game Orchestra has a YouTube channel with some of our past performances. One of my favorite arrangements is this medley of tracks from Paper Mario: The Thousand-Year Door -- expect some of my others to be posted soon too!

• Our final project of 21M.303, Writing in Tonal Forms I, was to compose a minuet and trio for string quartet. You can find the score for my composition here, as well as a recording of it performed by the Worcester Chamber Music Society.

• If you want to hear me play some chamber music with friends, feel free to check out these recital recordings from May 2022 (music composed by group members!) or December 2021. I am kind of rusty but the pieces are good!