Research interests

Current group members:

Faculty:

Megumi Harada enjoys working in equivariant symplectic and algebraic geometry, with particular attention to their interactions with combinatorics and representation theory. More specifically, her recent work has touched upon themes such as: integrable systems, toric degenerations, Newton-Okounkov bodies, Hessenberg varieties, and Schubert calculus.

Jenna Rajchgot works at the intersection of algebraic geometry, combinatorics, and commutative algebra. She is particularly interested in algebro-geometric and combinatorial properties of algebraic varieties which have large groups of symmetries (eg. Schubert varieties, quiver loci, symmetric varieties), as well as in techniques which are useful in their study (eg. degenerations, Groebner bases, Frobenius splitting, liaison).

Adam Van Tuyl's research area is commutative algebra and its connection to other areas like combinatorics and algebraic geometry. He is interested in homological invariants, edge ideals, simplicial complexes, sets of points in (multi)-projective spaces, toric ideals, symbolic powers of ideals, and combinatorial matrix theory.

Postdoctoral fellows:

Thanh Thai Nguyen is interested in commutative algebra and its interactions with combinatorics and geometry. His current research focuses on understanding symbolic powers of ideals and related invariants, especially symbolic powers of ideal of points and monomial ideals.

Graduate students:


Samples of past research projects:

PhD students

  • Graham Kieper (2022) Toric ideals of finite simple graphs. Supervisor: Adam Van Tuyl

  • Emmanuel Neye (2022) Groebner bases via linkage for classes of generalized determinantal ideals. Supervisor: Jenna Rajchgot

  • Lauren DeDieu (2016) Newton-Okounkov Bodies of Bott Samelson and Peterson Varieties. Supervisor: Megumi Harada

MSc students

  • Maryam Nowroozi (2021) Virtual Resolutions of points in P^1 x P^1 [Thesis] Supervisors: Megumi Harada and Adam Van Tuyl

  • Jarvis Kennedy (2020) An Algebraic Condition for a Complex to be Virtual [Project] Supervisors: Megumi Harada and Adam Van Tuyl

  • Michael Cox (2019) On Condition Numbers of Companion Matrices [Project] Supervisors: Kevin Vander Meulen and Adam Van Tuyl

  • Julia Gibson (2018) Rings of Conditions of Rank 1 Spherical Varieties [Thesis] Supervisor: Megumi Harada

Undergraduate Research Projects

  • Mike Cummings (2022) Symbolic defect of points in P^1 x P^1, Supervisor: Adam Van Tuyl [NSERC USRA]

  • Mike Cummings (2022) Geometric Vertex Decomposition and Hessenberg Patch Ideals, Supervisors: Sergio Da Silva, Megumi Harada, Jenna Rajchgot [Senior Thesis]

  • Adrian Cook (2021) Symbolic Defect of the cover ideals of disjoint graphs, Supervisor: Adam Van Tuyl [Senior Thesis]

  • Runyue Wang (2021) Minimal Resolutions of the Alexander dual of the van der Waerden Complex, Supervisors: Jenna Rajchgot and Adam Van Tuyl [Senior Thesis]

  • Fady Abdelmalek (2020) Well-Covered Token Graphs, Supervisors: Kevin Vander Meulen and Adam Van Tuyl [NSERC USRA]

  • Eden Petruccelli (2020) - Vertex Decomposability and Regularity of Down-Left Graphs, Supervisor: Adam Van Tuyl [Senior Thesis]

  • Esther Vander Meulen (2019) Well-Covered Token Graphs, Supervisors: Kevin Vander Meulen and Adam Van Tuyl [NSERC USRA]

  • Fady Abdelmalek (2019) Well-Covered Token Graphs, Supervisors: Kevin Vander Meulen and Adam Van Tuyl [NSERC USRA]

  • Prabin Niroula (2019) - Powers of Edge Ideals and their Multiplicities, Supervisor: Adam Van Tuyl [Senior Thesis]