I gave a mini-course (in 3 parts) on the mapping class group in the 2020 Geometric Group Theory without Boundaries summer school. My goal was for my lectures to be accessible to a junior grad student. Here is the youtube playlist of my recorded talks.

Advising: I am currently co-advising Becky Eastham who will graduate with her PhD in Spring 2024 and start a postdoc at UC Riverside in Fall 2024. Mateo Morales is also reading with me.

Geometry & Topology: 

13. Volumes of end-periodic mapping tori. (comments welcome) This is a preliminary draft of 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, to appear. [pdf], [arXiv]

10. A note on an effective characterization of covers with an application to higher rank representations. Groups, Geometry, and Dynamics, to appear. With Tarik Aougab, Max Lahn, and Nick Miller. [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, to appear. [pdf], [arXiv] 

8. Finding and Combining Indicable Subgroups of Big Mapping Class Groups. (submitted) With Carolyn R. Abbot, Hannah Hoganson, Rachel Skipper, and Priyam Patel. [pdf], [arXiv] 

7. End-periodic homeomorphisms and volumes of mapping tori. With Elizabeth Field, Heejoung Kim, and Christopher Leininger. Journal of Topology 16-1 (2023) 57--105. [pdf], [arXiv] 

6. Graphs of curves for surfaces with finite-invariance index 1. With Justin Lanier. Glasnik Matematicki 57-77 (2022) 119--128. [pdf], [arXiv] 

5. Characterizing covers via simple closed curves. With Tarik Aougab, Max Lahn, and Yang Xiao. Geometriae Dedicata 217-2 (2023) 26. [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 73-2 (2023) 305--343. [pdf], [arXiv] 

3. Centers of subgroups of big mapping class groups and the Tits alternative. With Justin Lanier. Glasnik Matematicki 55-1 (2020) 85--91. [pdf], [arXiv] 

2. Length spectra of flat metrics coming from q-differentials, Groups, Geometry, and Dynamics 14-4 (2020), 1223--1240. [pdf], [arXiv]

1. Least dilatation of pure surface braids (with an appendix coauthored by Hugo Parlier), Algebraic and Geometric Topology 19-2 (2019) 941--964. [pdf], [arXiv] 

Algebra & Combinatorics:

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, to appear. [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, to appear. [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, to appear. [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 27(5):641-662. [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 27(1) (2020), #P1.33. [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. 44 (2014), no. 6, 1817--1850 [arXiv]

* denotes an undergraduate author