Tristan Shin

I am currently a PhD student in Mathematics at UC San Diego. Prevoiusly, I completed my Bachelor of Science in Mathematics at MIT in June 2023 and my Master of Advanced Study in Pure Mathematics at the University of Cambridge (Part III of the Mathematical Tripos) in June 2024. My mathematical interests primarily lie in extremal/additive combinatorics and analytic number theory.

Research

In Summer 2025, I will be attending the IAS/Park City Mathematics Institute Graduate Summer School about Probabilistic and Extremal Combinatorics.

In the 2024-2025 academic year, under the supervision of Freddie Manners, I did various "Reading and Research" activities in additive combinatorics.

In Summer 2023, I worked on a project about sieve theory. Specifically, we studied the decomposition of certain sums into parts based on prime factorization structure. These sums show up when analyzing prime gaps using the Selberg sieve.

In Spring 2022, I worked on a project about Schubert polynomials and the symmetric group. This stemmed from a Directed Reading Program project about Manivel's book on symmetric functions.

In Summer 2020, I participated in the MIT Math Department's UROP+ program, working on the probability theory of a model of branched polymers. As part of the program, I wrote a paper explaining the some of the work that we did: On the space of planar branched polymers with fixed tangency graph.

Expository writing

I have written a handful of expository pieces, including:

Contests

I am/was involved in organizing a handful of math competitions:

As part of these, I wrote many problems at various difficulty levels. A small archive of some of them can eventually be found here.

I used to participate in math competitions, but that was way back in the day.

Teaching

I have taught in many different settings, including as a teaching assistant for courses and as an instructor for math programs.

Teaching Assistant

UCSD

MIT

Programs

I have also taught/managed at various programs, including the following:

Some of the handouts that I developed for these programs can be found here.

Courses taken

Combinatorics

  • UCSD Math 264B: Combinatorics II (Winter 2025)
  • UCSD CSE 291E: Additive Combinatorics and its Applications (Fall 2024)
  • Cambridge Part III Introduction to Additive Combinatorics (Lent 2024)
  • Cambridge Part III Ramsey Theory on Graphs (Michaelmas 2023)
  • MIT 18.212: Algebraic Combinatorics (Spring 2021)
  • MIT 18.226: Probabilistic Methods in Combinatorics (Fall 2020)
  • MIT 18.225[1]: Graph Theory and Additive Combinatorics (Fall 2019)
  • UCSD Math 184[2]: Enumerative Combinatorics (Winter 2018)

Theoretical Computer Science

  • Cambridge Part III Introduction to Computational Complexity (Lent 2024)
  • MIT 18.404: Theory of Computation (Fall 2020)
  • MIT 6.046: Design and Analysis of Algorithms (Fall 2019)

Algebra and Number Theory

  • UCSD Math 200C: Algebra III (Spring 2025)
  • UCSD Math 200B: Algebra II (Winter 2025)
  • UCSD Math 200A: Algebra I (Fall 2024)
  • Cambridge Part III Elliptic Curves (Lent 2024)
  • Cambridge Part III Modular Forms (Michaelmas 2023)
  • MIT 18.158: Analytic Number Theory (Spring 2023)
  • MIT 18.785: Number Theory I (Fall 2022)
  • MIT 18.704: Seminar in Algebra (Spring 2022)
  • MIT 18.784: Seminar in Number Theory (Fall 2021)
  • MIT 18.702: Algebra II (Spring 2020)
  • MIT 18.701: Algebra I (Fall 2019)

Analysis

  • UCSD Math 270C: Numerical Ordinary Differential Equations (Spring 2025)
  • UCSD Math 220B: Complex Analysis II (Winter 2025)
  • UCSD Math 270B: Numerical Approximation and Nonlinear Equations (Winter 2025)
  • UCSD Math 270A: Numerical Linear Algebra (Fall 2024)
  • Cambridge Part III Analysis of Partial Differential Equations (Michaelmas 2023)
  • Cambridge Part III Approximation Theory (Michaelmas 2023)
  • MIT 18.103: Fourier Analysis: Theory and Applications (Fall 2022)
  • MIT 18.031: System Functions and the Laplace Transform (IAP 2020)
  • UCSD Math 140C: Foundations of Real Analysis III (Spring 2019)
  • UCSD Math 140B: Foundations of Real Analysis II (Winter 2019)
  • UCSD Math 140A: Foundations of Real Analysis I (Fall 2018)
  • UCSD Math 120A: Elements of Complex Analysis (Fall 2017)

Probability and Statistics

  • UCSD Math 289A: Random Matrices (Spring 2025)
  • Cambridge Part III Stochastic Calculus and Applications (Lent 2024)
  • Cambridge Part III Stochastic Processes in Biology (Lent 2024)
  • MIT 18.650: Fundamentals of Statistics (Spring 2021)

Miscellaneous

  • MIT 18.A34: Mathematical Problem Solving (Fall 2019)
[1] Was 18.217 when I took it.
[2] Was Math 184A when I took it.