Research

I’m currently thinking about exponential random graph models (ERGMs) as they appear in mathematics. Traditionally, they are used to model social networks. They can be investigated from a mathematical perspective by asking whether this family of probability distributions satisfy some nice conditions, such as negative dependence. In this way, we connect geometry and probability theory. This connection was described in seminal work by Borcea, Brändén, and Liggett. My PhD thesis describes the interplay of these ideas as well as generalizations to other random (hyper)graph models. My latest preprint expands on these ideas and generalizes them in applications to real-world networks.

Achievements

• Ontario Graduate Scholarship in Science and Technology, Western University, 2022.
• Peter Rodney Prize for best student talk at the Ontario Combinatorics Workshop, University of Waterloo, 2022.
• Faculty of Science Graduate Student Teaching Award, Western University, 2020.
• Ontario Graduate Scholarship in Science and Technology, Western University, 2020.
• Faculty of Health Silver Medal for Academic Merit, York University, 2016.

Talks

Summer 2023

• Generating polynomials of exponential random graphs, PhD defense, August 2023 (slides)

Fall 2022

• The geometry of Markov random graphs, Geometry and Combinatorics Seminar, The University of Western Ontario, November 2022 (slides)

Summer 2022

• The geometry of random graphs with a Markov flavour, 26^th Ontario Combinatorics Workshop, University of Waterloo, May 2022 (slides)

Graduate & reading courses

Winter 2022

• Probability and Number Theory at Queens University via The Fields Institute
• Topos Theory (Reading Seminar).
  • Talk: Lattice and Heyting algebra objects in a topos

Fall 2021

• Topos Theory (Reading Seminar).
  • Talk: Sheaves as étale spaces and the inverse image sheaf
• Random Matrix Theory and Topological Recursion (Reading Seminar).

Summer 2021

• MATH 9171L: Mathematical Computation
  • Final presentation slides and recording

Winter 2021

• MATH 9141B: Commutative Algebra
• Homotopical Algebra (Reading Seminar). Talks:
  • The projective model structure on chain complexes
  • Reedy categories and diagrams

Fall 2020

• MATH 9163A: Convex Geometry

Winter 2020

• MATH 9020B: Field Theory
• MATH 9053B: Algebraic Geometry

Summer 2018

• MATH 9511L: Category Theory
• MATH 9140L: Representation Theory

Winter 2018

• MATH 9022B: Introduction to Measure Theory
• MATH 9051B: Algebraic Number Theory
• MATH 9052B: Algebraic Topology

Fall 2017

• MATH 9148A: Graph Theory: Expander Graphs
• MATH 9054A: Functional Analysis
• MATH 9023A: Rings and Modules