Mentoring

For undergraduate students

We organize mentoring for undergraduate students. Suppose you want to discuss your REU project with a graduate student, or you wish to attend graduate school in the future but have no idea what it looks like or how to apply. The following topics are structured reading groups for Spring 2025, but if you have a specific topic not listed here, feel free to reach out to Donovan to see if there’s interest.

Reading groups are open to all undergraduates and non-math majors are encouraged to join. These reading group topics can possibly turn into an honors thesis by expanding upon the work done with a faculty advisor.

Fill out this form to sign up for a reading group. You will be contacted shortly after.

If you have any comments or questions, contact Donovan Snyder.

Reading Group Topics for Spring 2025

Topics in Category Theory (Limited Space Available)

  • Organizer Siddharth Gurumurthy
  • Description: Depending on the student’s background, we’ll cover topics tailored to their interests (this can include some advanced topics like Monoidal structures, Monads or Simplicial sets) or we will discuss standard introduction to the subject: Categories, Functors, Limits and colimits, Adjunctions and the Yoneda Lemma. 
  • Prerequisites: Math 237 and 240, or equivalent.
  • Resources to be used: Depends on student, Category Theory in Context by Emily Riehl, Basic Category Theory by Tom Leinster.

Foundations of Harmonic Analysis

  • Organizers Zhihe Li, Ke Yu
  • Description: We will begin with the basics of Fourier analysis and functional spaces to study key concepts in harmonic analysis. The first five chapters of Thomas Wolff’s Lectures in Harmonic Analysis provide a detailed introduction to essential topics such as Schwartz space, Fourier transforms, and its related properties such as Fourier inversion and Plancherel. By the end of this semester, we will apply our knowledge in harmonic analysis to study some results in uncertainty principles and restriction problems.
  • Prerequisites: Analysis of 170’s or 265. The topics of the reading course will be adjusted to the level of the students.
  • Resources to be used: Lectures in Harmonic Analysis by Thomas Wolff.

Algebraic Methods in Probabilistic Models (Limited Space Available)

  • Organizer Donovan Snyder
  • Description: We’ll examine various probabilistic models and Markov chains (like the Ising Model, ASEP, six-vertex, and polymers) that can be analyzed through applications of algebraic methods. These are often called integrable systems in physics literature.
  • Prerequisites: Algebra of at least Math 236, and familiarity with probability (like 201, though not required)
  • Resources to be used: Depends on specific interest, Lectures on Integrable Probability by Borodin and Gorin, Exactly Solved Models in Statistical Mechanics by Baxter

For graduate students

Mentoring can help you build valuable skills which you will find useful throughout your career, whether you go into academia or industry.

If you want to join this program as a mentor for Spring 2025, contact Donovan.