Mentoring

For undergraduate students

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

For the Spring 2026 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.

Check out the choices for reading groups below, and check back soon for a link to sign up!

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

Reading Group Topics for Spring 2026

Introducing Polymer Models

  • Grad student organizer: Roan James
  • Description: The plan is to introduce the basics of polymer models. These can be seen as simple random walks (SRW) in an external medium/environment. We will start by recalling some of the basic properties of the SRW (transience/recurrence) and then proceed to define polymer models. If there is time, we can introduce the KPZ universality class.
  • Prerequisites: Math 201 is essential. Math 265 would be helpful but not required.
  • Resources to be Used: Random Walks and the Heat Equation - Greg Lawler

Arithmetic Dynamics

  • Grad student organizer: Daniel Gotshall
  • Description: Arithmetic dynamics generally studies patterns and properties of points formed from iteration of a polynomial or rational function starting at a given point in a field. Originally this area began by studying forward iterates over R and C, leading to the definitions of the complementary Julia and Fatou sets, which are simply the sets of points with chaotic and repetitive (preperiodic) behavior, respectively. This was then generalized to working over number fields, where one can form equivalence relations between pairs of rational functions and certain points. We will see theorems that can use a single member of the equivalence class to make conclusions on the dynamics of all maps in the class. Another topic will involve using “height functions” to quantify the size of the set of preperiodic points of rational maps under certain conditions. If time permits, we will study properties of the Galois extensions generated by adjoining certain preperiodic points. Current research is generally focused on the Galois theory arising from “preimages of points” (iterates done in the reverse direction).
  • Prerequisites: Math 230 and 237 are required. Some knowledge of equivalence relations/classes and projective space will be helpful, although we will review these concepts if anyone needs.
  • Resources to be Used: The Arithmetic of Dynamical Systems - Joseph Silverman

Introduction to Harmonic Analysis

  • Grad student organizers: Zhihe Li, Ke Yu
  • Description: In an effort to explore the foundations of harmonic analysis, we will begin with the basics of Fourier analysis and functional spaces to study key concepts in the subject. 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, 265H. The topics of the reading course will be adjusted to the level of the students.
  • Resources to be used: Lectures in Harmonic Analysis - Thomas Wolff

TBD

  • Grad student organizer: Luke Barbarita

TBD

  • Grad student organizer: Donovan Snyder

Groups from Previous Semesters

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.