Raj Gandhi


Email
rg593 "at" cornell.edu
Github
github.com/RajGandhi97
Address
Department of Mathematics
Malott Hall, Cornell University
301 Tower Rd, Ithaca, NY 14853, USA

I am a fifth-year Ph.D. student studying mathematics at Cornell University. My advisor is Allen Knutson.

I am interested in algebraic combinatorics, and especially in generalized Schubert calculus, Coxeter groups, brick manifolds, and recently matroids.

In 2021, I recieved a M.Sc. degree in mathematics from the Univerity of Ottawa. My M.Sc. advisors were Alistair Savage and Kirill Zainoulline.

In 2019, I received a B.Sc. in physics-mathematics from the University of Ottawa.

Publications/Conference Proceedings

  1. Raj Gandhi. Deforming the motivic Segre classes of Schubert cells in the Grassmannian. Séminaire Lotharingien de Combinatoire. (2025). Conference Proceeding.
  2. Raj Gandhi. (Joint with Gabe Udell ) A degeneration of the brick variety and a decomposition of the associahedron into cubes. Séminaire Lotharingien de Combinatoire. (2025). Conference Proceeding.
  3. Raj Gandhi. (Joint with Alistair Savage and Kirill Zainoulline). Diagrammatics for F4. Bulletin of the London Mathematical Society. (2022). DOI. Preprint.
  4. Raj Gandhi. The formal affine Demazure algebra and real finite reflection groups. Algebras and Representation Theory. (2022). DOI. Preprint.
  5. Raj Gandhi. Decomposing Frobenius Heisenberg categories. Journal of Algebra and its Applications. (2020). Vol. 19. No. 5. Pp. 2050094-1-2050094-31. DOI. Preprint.
M.Sc. thesis
  • Raj Gandhi. Oriented cohomology rings of the semisimple linear algebraic groups of ranks 1 and 2. (2021). University of Ottawa library. URL. Code.

Computer programs
  1. Raj Gandhi. Oriented cohomology rings of the semisimple linear algebraic groups of ranks 1 and 2. (Last updated: 2021).
  2. Raj Gandhi. Modularity and Calabi-Yau threefolds. (Last updated: 2020).

Cornell University: Teaching assistant
  1. MATH 1920: Multivariable Calculus for Engineers. Grader and recitation instructor. (Fall 2025).
University of Ottawa: Teaching assistant
  1. MAT 1320X: Calculus I. Recitation instructor. (Summer 2021).
  2. MAT 2355: Introduction to Geometry. Grader. (Winter 2021).
  3. MAT 1348: Discrete Mathematics for Computing. Grader and recitation instructor. (Winter 2021).
  4. MAT 2141: Honours Linear Algebra. Grader. (Fall 2020).
  5. MAT 1341: Introduction to Linear Algebra. Grader and recitation instructor. (Fall 2020).
  6. MAT 1332: Calculus II for the Life Sciences. Grader and recitation instructor. (Fall 2020).
  7. MAT 1300X: Mathematical Methods I. Recitation instructor. (Summer 2020).
  8. MAT 1320: Calculus I. Grader and recitation instructor. (Winter 2020).
  9. MAT 1348: Discrete Mathematics for Computing. Grader and recitation instructor. (Winter 2020).
  10. MAT 1362: Mathematical Reasoning and Proofs Grader. (Winter 2020).
  11. MAT 1362: Mathematical Reasoning and Proofs. Grader and recitation instructor. (Fall 2019).

Invited/Contributed talks
  1. Deforming the motivic Segre classes of Schubert cells in the Grassmannian. Algebra Seminar. University of Ottawa. June 26, 2025. Slides.
  2. Deforming the motivic Segre classes of Schubert cells in the Grassmannian. Combinatorics Seminar. University of Toronto. May 1, 2025. Slides.
  3. Degenerating brick manifolds and subdividing the associahedron. Graduate Student Combinatorics Conference. Carnegie Melon University. March 17, 2024.
  4. The formal group ring and real finite reflection groups. Algebra and Geometry of Homogeneous Spaces. University of Ottawa. June 3, 2021. Slides.

Posters
  1. Deforming the motivic Segre classes of Schubert cells in the Grassmannian. Formal Power Series and Algebraic Combinatorics. Hokkaido University. July 21, 2025. Poster.
  2. Deforming the motivic Segre classes of Schubert cells in the Grassmannian. Mid-Atlantic Algebra, Geometry, and Combinatorics Workshop. CUNY Graduate Center. March 22, 2025.
  3. Generalized cohomology rings of rank 2 root systems. Encuentro Colombiano De Combinatoria. Universidad del Cauca. June 26, 2024. Poster.
  4. The ring of twisted differential operators of reflection group I2(5). University of Ottawa UROP symposium. 2016. Poster.


Undergraduate talks
  1. The Heisenberg category. Student summer seminar. University of Ottawa. August 17, 2018. Slides.
  2. Twisted formal group algebras. Summer student seminar. University of Ottawa. August 16, 2017. Slides.
  3. Finite reflection groups. Junior algebra seminar. University of Ottawa. September 8, 2016. Slides.

Attended

  1. Workshop on algebra and representation theory. University of Oregon. August 18-22, 2025.
  2. Formal power series and algebraic combinatorics. Hokkaido University. July 21-25, 2025.
  3. Apprenticeship program in commutative algebra. Field's institute. January 20-24, 2025.
  4. Formal power series and algebraic combinatorics. Ruhr-Universität Bochum. July 22-26, 2024.
  5. Summer school in algebraic combinatorics. Max Planck Institute (Leipzig). July 15-19, 2024.
  6. Schubert summer school. University of Illinois at Urbana-Champaign. June 12-22, 2023.
  7. Algebraic geometry northeastern series. Stony Brook University. April 28-30, 2023.
  8. Route 81. Queen's University. September 24, 2022.
  9. The Los Angeles Workshop on Representations and Geometry. University of Southern California. June 6 - June 10, 2022.
  10. Cornell Topology Festival. Cornell University. May 6 - May 8, 2022.
  11. Derived Categories and Moduli Spaces. Cornell University. April 29 - May 1, 2022.

Organized

  1. What is ...? seminar. (Co-organized with Matej Neumann). Cornell University. Fall 2022.


A complete set of worksheets and notes from my outreach and service can be found here: worksheets and notes.
I do not claim full originality in any of these notes or worksheets. With that said, feel free to these in your own teaching!

Cornell Prison Education Program

The Cornell Prison Education Program provides courses leading to college degrees for people incarcerated in upstate New York prisons.

Spring 2025
I was an instructor for MATH 112, a course offered at Auburn Correctional Facility through Cayuga Community College. (Unfortunately, the course was cancelled partway through due to a correctional officer strike.)

Fall 2024
I was a tutor for MATH 112, a course offered at Auburn Correctional Facility through Cayuga Community College.

Ithaca High School Math Seminar

The IHS math seminar provides advanced Ithaca High School students with the opportunity to learn college-level mathematics from a graduate student instructor, and to take on a research project with the instructor at the end of the term.

Fall 2024
I taught a 16-lesson-long course on tropical geometry. Exercises.

Spring 2024
I taught a 16-lesson-long course on partially ordered sets and algebraic combinatorics. Notes.

Spring 2023
I taught a 16-lesson-long course on Young tableaux. Notes.

Canada/USA Mathcamp

Mathcamp is a five-week-long summer program for mathematically talented students ages 13-18.

Summer 2023
I was a mentor at Mathcamp. I taught the following courses:
Knot Invariants, Representation theory of the symmetric groups, Linear algebra through knots, Quiver representations II, and Introduction to Schubert calculus.
Additionally, Kevin Chang and I co-supervised a reading project introducing quantum groups to a group of campers.

GRASSHOPR

The GRASSHOPR program at Cornell University provides graduate students with the opportunity to create a mini-course (3-5 lessons) and teach the course at a local elementary, middle, or high school in Ithaca, NY.

March 2025
Anna Barth and I taught a three-lesson-long mini-course to middle schoolers on cryptography at Lehman Alternative Community School in Ithaca, NY. Worksheets: Cryptography.

March 2023
I taught a five-lesson-long mini-course to middle schoolers on graph theory at Lehman Alternative Community School in Ithaca, NY. Worksheets: Graph Theory.

March 2022
Aria Beaupré and I taught a four-lesson-long mini-course on voting theory at Namasté Montessori School in Ithaca, NY. Worksheets: The Mathematics of Decision Making.

Directed reading program

The directed reading program is organized by the Cornell mathematics department. The program pairs Cornell undergraduate students studying mathematics ("mentees") with Cornell mathematics Ph.D. students ("mentors"), who go on to read a mathematics textbook together for one semester.

Fall 2025
My two mentees and I are reading currently reading "Matroids: a Geometric Introduction" by Gary Gordan and Jennifer McNulty.

Spring 2023
My mentee and I read the first six chapters of "The Knot Book" by Colin Adams.

Fall 2022
My mentee and I read the first three chapters of "Arithmetic of Elliptic Curves" by Joseph H. Silverman.