Vertically Integrated Research
Each semester, the LSU Mathematics Department offers a number of Vertically Integrated Research (VIR) courses, which aim to bring together undergraduates, graduate students, postdocs, and senior faculty to learn about and work on current problems in mathematics.
In a VIR seminar, each undergraduate is typically paired with one junior and one senior graduate student to form a “mentorship group.” The graduate mentors will help guide the undergraduates (and one another!) as we all learn, process, present, and expand upon the mathematics. The postdocs and senior faculty keep track of everyone’s progress, ensuring that everyone understands their roles and is appropriately up-to-speed.
In addition to learning about modern mathematical research, students are trained to better communicate mathematics—what we call “mathematical fluency”. Mathematical fluency is about developing an intuitive understanding of what certain mathematical statements are saying, why they are true, and how they fit into the broader mathematical tapestry. Hand-in-hand with mathematical fluency is the ability to identify with, write to and speak to to one’s audience. We work with students to develop these skills through appropriate intensive oral and written assignments.
Below is a list of recent VIR courses that have been offered in topology, representation theory and mathematical physics.
Current Courses, Spring 2026
- C. Bibby and Z. Wang: Topics in Combinatorics.
- This is a project-based seminar class in combinatoraics. 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.
- P. Achar: Quantum cohomology
- Quantum cohomology is a topic with connections to classical problems in enumerative geometry as well as to modern ideas coming from mathematical physics, such as mirror symmetry and Gromov-Witten invariants. This course will be a beginners' introduction to these topics, with a focus on understanding the quantum cohomology of complex projective space.
Previous semesters
Fall 2025
- C. Bibby and K. Schreve: Combinatorial Topology
Spring 2025
- P. Dani and K. Schreve: Polyhedral complexes and their automorphism groups
Fall 2024
- P. Achar and A. Balibanu: Algebraic geometry for matroids
- P. Dani and K. Schreve: Groups with remarkable origins
- S. Vela-Vick: Integrated research on geometry and topology
Spring 2024
- C, Bibby and D. Cohen: TACI: Topological Algebraic and Combinatorial Interactions
- S. Vela-Vick and Wu
Fall 2023
- P. Achar: Cluster algebras
- C. Bibby and D. Cohen: TACI: Topological Algebraic and Combinatorial Interactions
- P. Dani and K. Schreve: Groups, graphs and beyond