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
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Over the past few months, I attended the following conferences:
- CanaDAM 2025 at the University of Ottawa, where I also gave a talk on patch ideals for (semisimple) Hessenberg varieties
- AlCoVE 2025
- Recent Trends in Commutative Algebra, an SMS Summer School at the Fields Institute
- Macaulay2 workshop at the University of Wisconsin–Madison, where I was part of a group working on software for Ehrhart Theory
- In November, I will attend Computation in Representation Theory, a workshop during the semester program Categorification and Computation in Representation Theory at ICERM
- I attend the University of Waterloo Algebraic and Enumerative Combinatorics Seminar and Tutte Colloquium.
- 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.
Teaching
For Spring 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