I am currently pursuing an M.Sc. in Mathematics, working on the probabilistic analysis of combinatorial objects under the supervision of Luc Devroye. My research interests include:

- probabilistic analysis of algorithms
- analysis of random discrete structures
- enumerative combinatorics
- additive combinatorics

### Papers

**P2.** (with Anna M. Brandenberger and Luc Devroye) Root estimation in Galton-Watson trees. To appear in
*Random Structures and Algorithms*, 24 pp.
[arXiv]

**P1.** (with Rosie Y. Zhao) Arithmetic subsequences in a random ordering of an additive set. *Integers: Electronic Journal of Combinatorial Number Theory* **21** (2021),
#A89, 19 pp.
[arXiv]

### Submitted papers

Papers submitted for publication in refereed journals.

☀ (with Luc Devroye and Rosie Y. Zhao) The independence number of a Bienaymé-Galton-Watson tree and related parameters. *arXiv preprint 2106.14389*, 20 pp.

☀ (with Jad Hamdan and Jonah Saks) The lattice of arithmetic progressions. *arXiv preprint 2106.05949*, 15 pp.

☀ (with Anna M. Brandenberger, Luc Devroye, and Rosie Y. Zhao) Leaf multiplicity in a Bienaymé-Galton-Watson tree. *arXiv preprint 2105.12046*, 11 pp.

### Reports

Various project and research reports. Some reports were written for internal distribution only, and are therefore not available for download.

**R4.** Finding regularity in Tlingit verb prefixes. Semester project report, McGill University (Montréal, Québec, April 2021), 7 pp.

**R3.** Grid-building algorithms on manifolds. Summer research report, McGill University (Montréal, Québec, August 2020), 10 pp.

**R2.** Typechecking proof scripts: making interactive proof assistants robust. Honours project report, McGill University (Montréal, Québec, December 2019), 10 pp.

**R1.** The OPythn programming language. Software project report, Charles University (Prague, Czech Republic, June 2019), 10 pp.

### Sequences

I contributed the following sequences to the OEIS:

- A347580: The number of chains of length $k$ in the poset of all arithmetic progressions contained in \(\{1,\ldots,n\}\) of length in the range $[1.\,.n-1]$, ordered by inclusion.
- A341822: The longest known length of a 2-increasing sequence of positive integer triples with entries $\leq n$.
- A339942: Triangle read by rows: $T(n,k)$ is the number of permutations of the cyclic group \({\bf Z}/n{\bf Z}\) whose longest embedded arithmetic progression has length $k$.
- A339941: Triangle read by rows: $T(n,k)$ is the number of permutations of \(\{1,\ldots,n\}\) whose longest embedded arithmetic progression has length $k$.
- A338993: Triangle read by rows: $T(n,k)$ is the number of $k$-permutations of \(\{1,\ldots,n\}\) that form a non-trivial arithmetic progression, $1\leq k\leq n$.
- A338550: The number of binary trees of height $n$ such that the number of nodes at depth $d$ equals $d+1$ for every $d\in {0,\ldots,n}$.
- A335562: The number of unlabelled unary-binary trees with $n$ nodes such that every node with two children has children of different subtree sizes.

### Summer 2020

I received an NSERC Undergraduate Summer Research Award for Summer 2020. I worked with Asa Kohn under the supervision of Michael Lipnowski, designing and implementing sorting algorithms on manifolds with the goal of efficiently building grids on these spaces.

### COMP 400 Honours Project in Computer Science

During the Fall 2019 semester, I undertook a project in the Computation and Logic lab under the supervision of Brigitte Pientka. I worked with Jacob Errington to develop a typechecking algorithm for the Harpoon proof language as well as a translation procedure to convert Harpoon proof scripts into programs in the Beluga programming language. The summary of the work I helped with can be found in the slides to my end-of-term presentation, and my full report is available for download as well.