Mike Cummings
I am a PhD student in the Department of Combinatorics and Optimization at the University of Waterloo, working under the supervision of Oliver Pechenik.
In 2024, I received my master's degree from McMaster University, where my supervisor was Jenna Rajchgot. My master's thesis studied classes of Hessenberg varieties using patch ideals.
Research
Broadly, my research is in combinatorial algebraic geometry, often making use of computational tools. I have recently been thinking about: geometric vertex decomposition, Frobenius splitting, Hessenberg varieties, toric ideals of graphs, and matrix Schubert varieties.
My research is partially supported by an NSERC Canada Graduate Scholarship and a University of Waterloo President's Graduate Scholarship.
Activities
- I contributed to Macaulay2 version 1.25.05 the package IntegerProgramming, which uses Gröbner bases to solve integer linear programs. This was written as part of a project for Mike Stillman's course on computational commutative algebra and algebraic geometry during the commutative algebra thematic program at the Fields Institute in Winter 2025.
- At CanaDAM 2025, I gave a talk on patch ideals for (semisimple) Hessenberg varieties
- I also attended AlCoVE 2025
- In June, I will attend the summer school on Recent Trends in Commutative Algebra at the Fields Institute
- At the end of June, I will attend the Macaulay2 workshop at the University of Wisconsin–Madison
- I attend the University of Waterloo Algebraic and Enumerative Combinatorics Seminar and Tutte Colloquium.
Teaching
For Spring/Summer 2025, I am a TA for Geometry – Math 661, a course in the Master of Mathematics Teaching program at the University of Waterloo's Centre for Education in Mathematics and Computing.
Contact
Mike Cummings
he/him/his
mike [dot] cummings [at] uwaterloo [dot] ca
Mathematics and Computer 6311
Department of Combinatorics and Optimization
University of Waterloo
200 University Ave W
Waterloo, Ontario, Canada N2L 3G1