Mathematics

I am a Lecturer with the Centre for Education and Computing (CEMC) and an Adjunct Professor in the Pure Mathematics department at the University of Waterloo. From 2020 to 2022 I was a CIRGET Postdoctoral Fellow in the Department of Mathematics at the Université du Québec à Montréal, working with Steve Boyer and Duncan McCoy. In 2018 and 2019 I was a PIMS Postdoctoral Fellow in the Department of Mathematics at the University of Manitoba, working with Adam Clay. I completed my MMath in 2012, and my PhD in 2017 in the Department of Pure Mathematics at the University of Waterloo under the supervision of David McKinnon and Doug Park.

Research

My research interests are in mapping class groups, low dimensional topology, and ordered groups.

Publications and Preprints:

10. Rigidity of braid group actions on R and of low-genus mapping class group actions on S^1. [preprint, arXiv]
with Idrissa Ba and Adam Clay
Submitted.

9. Cofinal elements and fractional Dehn twist coefficients. [preprint, arXiv]
with Adam Clay
To appear in International Mathematics Research Notices.

8. Circularly ordering direct products and the obstruction to left-orderability. [journal, arXiv]
with Adam Clay
Pacific Journal of Mathematics, 312-2 (2021), 401-419

7. Homeomorphic subsurfaces and the omnipresent arcs. [journal, arXiv]
with Federica Fanoni and Alan McLeay.
Annales Henri Lebesgue, Volume 4 (2021), 1565-1593

6. Promoting circular-orderability to left-orderability. [journal, arXiv]
with Jason Bell and Adam Clay
Annales de l'institut Fourier, 71 (2021), no. 1, 175-201

5. Big Torelli groups: generation and commensuration. [journal, arXiv]
with Javier Aramayona, Autumn E. Kent, Alan McLeay, Jing Tao, and Rebecca R. Winarski
Groups, Geometry, and Dynamics, 13 (2019), no. 4, 1373-1399

4. Free products of circularly ordered groups with amalgamated subgroup. [journal, arXiv]
with Adam Clay
Journal of the London Mathematical Society (2), 100 (2019), 775-803

3. Mapping class groups of covers with boundary and braid group embeddings. [journal, arXiv]
with Alan McLeay
Algebraic & Geometric Topology, 20 (2020), 239-278

2. Lifting homeomorphisms and cyclic branched covers of spheres. [journal, arXiv]
with Rebecca R. Winarski
Michigan Mathematical Journal, 66 (2017), no. 4, 885-890

1. The liftable mapping class group of balanced superelliptic covers. [journal, arXiv, erratum]
with Rebecca R. Winarski
New York Journal of Mathematics, 23 (2017), 133-164

PhD Thesis: The liftable mapping class group. [pdf]

Master's Project: Intersection forms on Fermat hypersurfaces in complex projective space. [pdf]

Research

Research Statement

CV

Publications and Preprints:

Mathematical Family, Coauthors, and Friends