(click course name to display a short description)
Current and Upcoming
Math 7590 Topics in Geometry and Algebraic Topology: Rational Homotopy Theory
- Spring 2026
- Prerequisite: Strongly recommend some familiarity with homotopy theory (as in Math 7520 Algebraic Topology) and differential forms (as in Math 7550 Differential Geometry)
- Text: Rational Homotopy Theory and Differential Forms by Griffiths and Morgan (pdf free through LSU Library)
- Description: The course will start with some basics of homotopy theory, fibrations, Postnikov towers, and de Rham cohomology. The goal is then to study the rational homotopy type of a simply-connected space X, which is the homotopy type of its localization (or rationalization). The homotopy and homology groups of the rationalization are rationalizations of those for X, killing all torsion. The rational homotopy type of X has the advantage of being more computable than the (ordinary) homotopy type of X, thanks to algebraic models (using differential graded algebras or Lie algebras) from Sullivan and Quillen. The story is more complicated when X is not simply connected, when one needs to make sense of how to "rationalize" the (possibly non-abelian) fundamental group.
Math 4997 Vertically Integrated Research in Combinatorics (with Zhiyu Wang)
- Spring 2026
- Prerequisite: Linear Algebra (Math 2085 or 2090)
- Description: This is a project-based seminar class in combinatorics. Students work together in small groups to tackle problems in topics such as graph theory, matroid theory, order theory, enumerative and algebraic combinatorics, geometric and topological combinatorics. Previous experience in combinatorics is not required.
Previous Teaching Experience
At Louisiana State University:
Math 1550 Calculus I
- Fall 2020
Math 2085 Linear Algebra
- Spring 2023, Spring 2025
- Corequisite: Calculus I (previously, Calculus II was a prerequisite)
- Text: Linear Algebra with Applications by Otto Bretscher
- Description: Topics include systems of linear equations, vector spaces, linear transformations, matrices, and determinants.
Math 2090 Differential Equations and Linear Algebra
- Spring 2022 (x2)
Math 4997 Vertically Integrated Research: Geometry and Combinatorics of Polynomials (with Dan Cohen)
- Fall 2022, Spring 2023
- Description: Properties (unimodality, log-concavity,...) of polynomials which arise naturally in combinatorial settings (e.g., the chromatic polynomial of a graph).
Math 4997 Vertically Integrated Research: Topological, Algebraic, and Combinatorial Interactions (with Dan Cohen)
- Fall 2023, Spring 2024
- Prerequisite: Linear Algebra (Math 2085 or 2090)
- Description: This course will explore interactions between topology, algebra, and combinatorics. Topics may include, for example, Latin squares and associated groups, nets, special families of plane curves, block designs, and neighborly partitions, as well as their implications for a variety of subjects, including the theory of hyperplane arrangements and matroids, coding theory, etc.
Math 4997 Vertically Integrated Research in Combinatorial Topology (with Kevin Schreve)
- Fall 2025
- Prerequisite: Linear algebra; experience with topology or graph theory may be useful but not required
- Description: This is a project-based seminar class in geometry and topology. Students work together in small groups to tackle problems in combinatorial topology and geometric combinatorics. We will specifically focus on minimal flag triangulations of surfaces.
Math 7400 Combinatorial Theory
- Fall 2025
- Prerequisite: Calculus (Math 1552), Linear Algebra (Math 2085), and Abstract Algebra (Math 4200)
- Text: Enumerative Combinatorics Volume 1 by Stanley (pdf free through LSU Library)
- Description: Problems of existence and enumeration in the study of arrangements of elements into sets; combinations and permutations; other topics such as generating functions, recurrence relations, inclusion-exclusion, Polya's Theorem, graphs and digraphs, combinatorial designs, incidence matrices, partially ordered sets, matroids, finite geometries, Latin squares, difference sets, matching theory.
- Format: inquiry-based learning (IBL)
Math 7510 Topology I
- Fall 2022, Fall 2023
- Prerequisite: Advanced Calculus (Math 4031)
- Text: Topology (2nd ed.) by James R. Munkres and Algebraic Topology by Allen Hatcher
- Description: This course is a preparation course for the core qualifying examination in topology. It will cover general (point set) topology, the fundamental group, and covering spaces. We will also introduce simplicial complexes and manifolds.
Math 7590 Topics in Geometry and Algebraic Topology: Arrangements and Configuration Spaces
- Fall 2021
Math 7590 Topics in Geometry and Algebraic Topology: Combinatorial Algebraic Topology
- Fall 2024
- Prerequisite: Math 7512 Topology II
- Text: Combinatorial Algebraic Topology by Kozlov
- Description: We will learn about some fundamental tools for computing algebraic invariants of a topological space with an underlying combinatorial structure (eg. a partially ordered set). Topics may include, as time and interest allows, discrete Morse theory, shellability, sheaf theory, (homotopy) colimits, and spectral sequences.
At the University of Michigan:
- Math 115 Calculus I : Fall 2017 (x2)
- Math 217 Linear Algebra : Winter 2018 (x2), Fall 2018 (x2)
- Math 465 Intro to Combinatorics : Winter 2019 (x2), Fall 2019 (x2), Winter 2020 (x2)
At the University of Western Ontario:
- Calc 1000A Calculus I : Fall 2015
- Math 1228B Methods of Finite Math : Winter 2016
- Math 1600A Linear Algebra I : Summer 2016
- Math 2151A Discrete Structures for Engineering : Fall 2016
At the University of Oregon:
- Math 111 College Algebra : Fall 2009, Winter 2010, Spring 2010, Summer 2010, Fall 2011, Fall 2012 (x2)
- Math 112 Elementary Functions : Winter 2013
- Math 242 Business Calculus II : Winter 2011 (TA), Spring 2011 (TA), Summer 2012
- Math 243 Statistics : Fall 2010 (TA), Summer 2011
- Math 251 Calculus I : Winter 2012, Spring 2012, Fall 2013, Fall 2014
- Math 252 Calculus II : Winter 2014, Winter 2015
- Math 315 Elementary Analysis : Spring 2015