Mentoring

For undergraduate students

The graduate students of the Math Department at the University of Rochester offer 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.

For the Fall 2025 semester we are running a reading groups program, where you can learn about a topic by reading books or papers under the guidance of a graduate student. These reading group topics can possibly turn into an honors thesis by expanding upon the work done with a faculty advisor. Reading groups are open to all students and non-majors are encouraged to join.

Sign up for a reading group by filling out this form. We will reach out to you by September 5!

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

Reading Group Topics for Fall 2025

Topics in Category Theory

  • Grad student organizer: Siddharth Gurumurthy
  • Description: The preliminary plan is to talk about the basic concepts in category theory: categories, functors, the Yoneda lemma, (co)limits and adjunctions with a bunch of examples. The plan is subject to change and will depend on the available time and the interests of the participant(s).
  • Prerequisites: Math 236 is required. Math 237 and 240 will help substantially.
  • Resources to be Used: Notes on Category Theory - Paolo Perrone, Category Theory in Context - Emily Riehl, Basic Category Theory - Tom Leinster.

High-Dimensional Figures and Mapping Degree

  • Grad student organizer: Lippus Liu
  • Description: One might find it easy to think about figures in a 2-dimensional plane. Imagining figures in a 3-dimensional space might also be not that hard. But what if we move to 4-dimensional spaces, or 5, 6, or even higher? Imagination in these cases turns out to be not very helpful. To solve this problem, topologists developed so-called “topological invariants”, which can normally be derived by just computations. In this reading group, we will learn about a particular example, that is the mapping degree, which can be used to distinguish mappings between high-dimensional figures.
  • Prerequisites: Some basic multi-variable calculus (MATH 164/174) and point-set topology (MATH 240) is required. Some knowledge to manifolds will be helpful.
  • Resources to be Used: Topology from the differentiable viewpoint - John Milnor

Algebraic Methods to solve Probabilistic Models

  • Grad student organizer: Donovan Snyder
  • Description: The area of “integrable probability” is the study of systems that can be studied and analyzed using algebra: sometimes complicated group and Lie theory, but often times more simple procedures. We’ll deal with those more simple procedures to look at examples such as ASEP, the Polymer, and Six-Vertex models and answer basic questions.
  • Prerequisites: We will need to know the ideas of probability (MATH 201) and will freely use multi-variable calculus and linear algebra (MATH 164,165,235). The ideas of algebra (MATH 236) will be very helpful.
  • Resources to be Used: Depends on the interest of the student, but likely Lectures on integrable probability - Borodin and Gorin, Random polymers via orthogonal Whittaker and symplectic Schur functions - Bisi, Stochastic six-vertex model - Borodin, Corwin, and Gorin

For Graduate Students

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

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