For a relatively gentle introduction to my research area, check out this 3-part mini-course I gave on the mapping class group as part of the 2020 Geometric Group Theory without Boundaries summer school. My goal was for my lectures to be accessible to a junior grad student.
14. A lower bound on end-periodic stretch factors. With Chenxi Wu. Proceedings of the AMS, to appear. [pdf], [arXiv]
13. Volumes of end-periodic mapping tori. (comments welcome) This is an expository paper that will appear in the proceedings of the 2023 Riverside Workshop in Geometric Group Theory. [pdf]
12. A lower bound on volumes of end-periodic mapping tori. (submitted) With Elizabeth Field, Autumn Kent, and Christopher Leininger. [pdf], [arXiv]
11. Unmarked simple length spectral rigidity for covers. With Tarik Aougab, Max Lahn, and Nick Miller. Mathematische Annalen (2025). [pdf], [arXiv]
10. A note on an effective characterization of covers with an application to higher rank representations. With Tarik Aougab, Max Lahn, and Nick Miller. Groups, Geometry, and Dynamics, to appear. [pdf], [arXiv]
9. The braid index of n-bridge braids. With Dane Gollero*, Siddhi Krishna, Viridiana Neri*, Izah Tahir*, and Len White*. Journal of Knot Theory and its Ramifications (2023). [pdf], [arXiv]
8. A new construction of subgroups of big mapping class groups. (submitted) With Carolyn R. Abbott, Hannah Hoganson, Rachel Skipper, and Priyam Patel. [pdf]
7. End-periodic homeomorphisms and volumes of mapping tori. With Elizabeth Field, Heejoung Kim, and Christopher Leininger. Journal of Topology (2023). [pdf], [arXiv]
6. Graphs of curves for surfaces with finite-invariance index 1. With Justin Lanier. Glasnik Matematicki (2022). [pdf], [arXiv]
5. Characterizing covers via simple closed curves. With Tarik Aougab, Max Lahn, and Yang Xiao. Geometriae Dedicata (2023). [pdf], [arXiv]
4. Automorphisms of the k-curve graph. With S. Agrawal, T. Aougab, Y. Chandran*, J. R. Oakley*, R. Shapiro*, and Y. Xiao. Michigan Mathematical Journal (2023). [pdf], [arXiv]
3. Centers of subgroups of big mapping class groups and the Tits alternative. With Justin Lanier. Glasnik Matematicki (2020). [pdf], [arXiv]
2. Length spectra of flat metrics coming from q-differentials, Groups, Geometry, and Dynamics (2020). [pdf], [arXiv]
1. Least dilatation of pure surface braids (with an appendix coauthored by Hugo Parlier), Algebraic and Geometric Topology (2019). [pdf], [arXiv]
6. On (t,r) broadcast domination of certain grid graphs. With Natasha Crepeau*, Pamela E. Harris, Sean Hays*, Joseph Rennie, Gordon Rojas Kirby, and Alexandro Vasquez*. Involve (2023). [arXiv]
5. Visualizing the support of Kostant's weight multiplicity formula for the rank two Lie algebras. With Pamela E. Harris, Juan Ramirez*, Joseph Rennie, Gordon Rojas Kirby, Eduardo Torres Davila*, and Fabrice O. Ulysse*. Involve (2024). [arXiv]
4. On Kostant's weight q-multiplicity formula for sl_4(C). with Rebecca E. Garcia, Pamela E. Harris, Lucy Martinez*, David Melendez*, Joseph Rennie, Gordon Rojas Kirby, and Daniel Tinoco*. Applicable Algebra in Engineering, Communication and Computing (2022). [arXiv]
3. Weight q-multiplicities for representations of the exceptional lie algebra g_2. With Jerrell Cockerham*, Melissa Gutierrez Gonzalez*, Pamela E. Harris, Amaury Miniño*, Joseph Rennie, and Gordon Rojas Kirby. Bulletin of the Belgian Mathematical Society (2020). [arXiv]
2. A generalization of parking functions with backward movement. With Alex Christensen*, Pamela E. Harris, Zakiya Jones*, Andres Ramos Rodriguez*, Joseph Rennie, and Gordon Rojas Kirby. The Electronic Journal of Combinatorics (2020). [arXiv]
1. Non-stable K-theory for Leavitt path algebras. With Damon Hay, Martin Montgomery, Efren Ruiz and Katherine Todd*. Rocky Mountain Journal of Mathematics (2014). [arXiv]
* denotes an undergraduate author