Howdy!

I am a PhD student in mathematics at The University of Pennsylvania, and was formerly an undergraduate at The University of Texas at Austin. My main interests lie in geometric analysis and partial differential equations--especially concerning spaces of low-regularity, geometric measure theory, and lower curvature bounds. My recent work has largely concerned almost-rigidity problems and the structure of limit spaces.

I am currently (pun intended) on the academic job market during the 2024-2025 year :)

- My email is hstuff AT sas DOT upenn DOT edu
- For my CV, click here. Current-ish (pun also intended) as of October 2024.
- My PhD advisor is Davi Maximo, and my undergraduate advisors were Francesco Maggi and Salvatore Stuvard.

- Stability of Convex Disks (2023). Preprint: arXiv:2301.13130. Accepted in Calc. Var. PDE Sept. 2023
- Stability of Convex Spheres (Joint with Davi Maximo) (2023). Preprint: arXiv:2312.13995. Submitted.
- Width Stability of Rotationally Symmetric Metrics (Joint with Paul Sweeney Jr.) (2024). Preprint: arXiv:2409.13646. Submitted.

- Gender Minorities in Topology and Related Areas Konference (GeMTraK) at U-Penn. Spring 2024. See the link for more details.

- Joint Mathematics Meetings: Special Session on Metric Geometry and Topology. January 2025.
- Rutgers Geometric Analysis Seminar. December 2024.
- Lehigh Geometry Seminar. November 2024.
- Carnegie Mellon Graduate/Postdoc Seminar. November 2024.
- Convergence or Scalar Curvature (COSC) Seminar. October 2024.
- North Carolina State University Geometry-Topology Seminar. September 2024.
- Temple Graduate Student Conference in Algebra, Geometry, and Topology. May 2024.
- Temple Graduate Student Conference in Algebra, Geometry, and Topology. May 2023.
- Brown Workshop on Differential Geometry. March 2023.
- CUNY Geometric Analysis Seminar. March 2023.
- UPenn Geometry Seminar. March 2023.
- Australian Geometric PDE Seminar. October 2022.

- During the 2024-2025 academic year, I am a Graduate Fellow for Inclusive & Equitable Teaching with the Center for Excellence in Teaching, Learning, and Innovation (CETLI) at UPenn. See here for more information including related events, workshops, and resources.
- Fall 2024: I am teaching Math 1080: Mathematics of Change Pt. II.
- Summer 2024: I am teaching Math 2410: Introduction to PDEs.
- Spring 2024: I am teaching Math 1080: Mathematics of Change Pt. II.
- Fall 2023: I am on fellowship. For prior courses taught see my CV.

Office Hours: Mondays 1:15-2:15 DRL 3N2D

Collected below are a small potpourri of expositional pieces and notes I've written up. I hope they might be of some help, and I may upload more later. If you happen to come across any typos or errors, please let me know.

- Allard Type Regularity Theorems for Rectifiable Varifolds. My undergraduate thesis at UT Austin, under the supervision of Francesco Maggi and Salvatore Stuvard (2019). This could probably also serve as an introduction to the regulartity theory of rectifiable varifolds.
- The Yamabe Problem. A set of notes I wrote for a series of talks at UPenn, based on the (wonderful) paper by Lee and Parker, and the (wonderful) set of notes by Robin Neumayer.
- Intro to the Bochner Method. A set of notes I wrote for a series of talks at UPenn.
- Intro to the Hodge Theorem. A set of notes I wrote for a series of talks at UPenn.

I do stuff other than math!
In particular I play the bass trombone and electric bass, and am generally very excited about music.

You can hear me play trombone in the Penn Symphony Orchestra (Link) at one of our four yearly concerts which are free to attend! We have recently played Mahler Symphonies 1 and 2, Rachmanninov's Symphony 2 and Symphonic Dances, Tchaikovsky's Symphony 5, Sibelius' Symphony 2, Rimsky-Korsakov's Scheherazade, Mussorgsky-Ravel's Pictures at an Exhibition, and soooo much more.

If you hear me playing bass you've wandered into a west philly punk jam situation and should consider taking evasive action.