Hi there!

I'm a second year PhD student studying pure mathematics at Harvard, working on Fukaya categories and homological mirror symmetry under Denis Auroux. In addition to my research I also teach.

With Rafael Saavedra, I'm convening the Trivial Notions seminar for 2022-2023.

Publications and Preprints

• Ryan Ahern, Mathew Zuparic, Keeley Hoek, and Alexander Kalloniatis. Unifying warfighting functions in mathematical modelling: Combat, manoeuvre, and C2.
  Journal of the Operational Research Society, 2021.
• Alexander C. Kalloniatis, Keeley Hoek, Mathew Zuparic, and Markus Brede. Optimising structure in a networked Lanchester model for fires and manoeuvre in warfare.
  Journal of the Operational Research Society, 72(8):1863–1878, 2020.
• Richard Taylor, Alexander C. Kalloniatis, and Keeley Hoek. Organisational hierarchy constructions with easy Kuramoto synchronisation.
  Journal of Physics A: Mathematical and Theoretical, 53(8):085701, 2020.
• Mathew Zuparic and Keeley Hoek. Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation.
  Communications in Nonlinear Science and Numerical Simulation, 73:275–290, 2019.

Honours Thesis

Here is my honours thesis, Drinfeld centers for bimodule categories. It was supervised by Professor Scott Morrison at the Australian National University.

At the conclusion of my honours year I gave a colloquium-style talk on some results from the second chapter.

Notes

• Crash course: constructions in point-set topology and linear algebra

Graduate Reports

• The Stone–von Neumann–Mackey theorem: Quantum mechanics in functional analysis

• Rosenberg's reconstruction theorem: A path to noncommutative algebraic geometry

Undergraduate Essays

• A spectral entrée to the Ergodic theory proper, lightly seasoned with a physical perspective

• Why study algebras over functors? Algebras, Monads, and the proof of Beck's monadicity theorem

• Noncommutative vector bundles: The Greatest Hits™ of the K-theory of C*-algebras

• Monoidal ∞-categories over ∞-operads: Elements of Higher Algebra

• Rewrite heuristics and pair exploration for automated theorem proving

• Transfers and tom Dieck splitting, via the Wirthmüller isomorphism