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.
Sasha Zotine's work is centred around applications of vector bundles in algebraic geometry. Their recent work includes computations of derived pushforwards in toric geometry and dynamical results on classifying endomorphisms of projective bundles. They make frequent use of the mathematical software Macaulay2 to aid their research.
Silas Vriend is working on finding new examples and furthering the foundations of the new theory of polyptych lattices developed by Escobar-Harada-Manon.
Thanh Thai Nguyen (2022-24)
Jay Yang (2021-22)
Sergio Da Silva (2020-22)
Jeremy Lane (2019-22)
Johannes Hofscheier (2017-19)
Federico Galetto (2015-18)
Craig Kohne (2024) Monomial ideals with a prescribed Waldschmidt constant. Supervisor: Antoine Deza and Adam Van Tuyl
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
Illya Kierkosz (2024) Type A quiver varieties and positroid varieties [Thesis] Supervisors: Megumi Harada and Jenna Rajchgot
Mike Cummings (2024) Hessenberg ideals, geometric vertex decomposition, and Grobner bases [Thesis] Supervisors: Megumi Harada and Jenna Rajchgot
Busra Atar (2023) Hessenberg patch ideals of codimension 1 [Thesis] Supervisors: Megumi Harada and Jenna Rajchgot
Kieran Bhaskara (2023) Comparing invariants of toric ideals of graphs [Thesis] Supervisor: Adam Van Tuyl
Adrian Cook (2023) Duality and dualizability of rank-2 two-vertex lattice groupoids [Thesis] Supervisors: Megumi Harada and Jenna Rajchgot
Runyue Wang (2023) Frobenius Splittings for the toric ideals of graphs and ladder determinantal ideals. Supervisors: Jenna Rajchgot and Adam Van Tuyl
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
Will Prangley (2025) Bier Spheres, Supervisor: Adam Van Tuyl [Senior Thesis]
Justin Gebel (2025) Frobenius Splittings for Toric Ideals of Bipartite Graphs. Supervisors: Jenna Rajchgot, Adam Van Tuyl [Senior Thesis]
Leona Tilis (2024) Nonsymmetric Strong Multiplicity Property. Superivsors: Keven Vander Meulen, Adam Van Tuyl [NSERC USRA]
Abhilash Saha (2024) Nonsymmetric Strong Multiplicity Property. Superivsors: Keven Vander Meulen, Adam Van Tuyl [MITACS USRA]
Antonio Nigrio (2024) Hilbert polynomials of toric ideals of bipartite graphs. Supervisors: Jenna Rajchgot, Adam Van Tuyl [Senior Thesis]
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]