Here are the notes and/or slides for talks I have given, as well as expository stuff that I have written. Please send me an email if you find any typos/mistakes!

## Talk Slides

- An Overview of Algebraic Topology. I gave an introductory talk on algebraic topology and homotopy theory for the Math Club at UT Austin in Spring 2017.
- Algebraic Methods for Computing Picard Groups. I gave this expository talk at the Graduate Student Topology & Geometry Conference at UIUC in March 2019, as well as the YTM at EPFL in July 2019.
- The nilpotency of elements of the stable homotopy groups of spheres. I gave a talk on Nishida's paper of the same title for the eCHT Kan Seminar in Fall 2019.
- Invertible Objects: An Elementary Introduction to Picard Groups. I gave an introductory talk on Picard groups for the Math Club at UT Austin in Spring 2020.
- Applications of Group Cohomology to 3-manifolds. I gave this talk for the junior topology seminar at UT Austin in Spring 2020.
- Picard Groups of Stable Module Categories. I gave this talk for the GROOT Summer Seminar online in Summer 2020. Video available here.
- I co-taught the Summer Minicourse "Spectral Sequence Training Montage", with Arun Debray. I ran problem sessions, and gave two and a half talks on:
- Picard Groups of the Stable Module Category for Quaternion Groups. I gave a short research statement for the electronic Algebraic Topology Employment Network online in Fall 2020. The video is posted here.
- Picard Groups of the Stable Module Category for Quaternion Groups. I gave this research talk at the (virtual) UChicago-Northwestern Topology seminar, the UIUC Topology Seminar, and the OSU homotopy theory seminar.
- The Periodicity Theorem, Part I. I gave a talk on Section 9.1 of the Hill-Hopkins-Ravenel paper "On the non-existence of elements of Kervaire invariant one" for the eCHT Kervaire Invariant One Reading Seminar in Fall 2020.
- Picard Groups of the Stable Module Category for Quaternion Groups. I gave a gave this research talk at the Graduate Student Topology and Geometry Conference in Spring 2021.

## Talk Notes

- Simple Homotopy Theory and Whitehead Torsion. I gave this talk for the homotopy theory student seminar on algebraic K-theory at UT Austin in Fall 2016.
- Modular Representation Theory and Phantom Maps. I gave this talk for the student geometry seminar at UT Austin in Fall 2016.
- Taylor Towers and Snaith Splitting. I gave this talk for the homotopy theory student seminar on Goodwillie Calculus at UT Austin in Fall 2017.
- The Structure of Stable Homotopy Theories. I gave a talk on the first two sections for the student geometry seminar at UT Austin at UT Austin in Fall 2017.
- Nilpotence in Stable Homotopy Theory. I gave two talks for the homotopy theory student seminar on Nilpotence and Descent at UT Austin in Spring 2018.
- Picard Groups. I gave this talk for the student geometry seminar at UT Austin in Fall 2018.
- Algebraic Methods for Computing Picard Groups. I gave this talk for my oral candidacy exam at UT Austin in Fall 2018.

## Expository/Outreach

- The Group Structure of the Rubik's Cube. I wrote the first draft in Fall 2015 for Math 551 at Rutgers. A version appeared in the Spring 2015 issue of Principia, the Princeton Undergraduate Mathematics Journal.
- Surfaces, Space, and Hyperspace: An exploration of 2, 3, and higher dimensions. I gave an inquiry-based talk on surfaces and higher dimensions for the Saturday Morning Math Group (SMMG) at UT Austin in Spring 2018.
- Number Games. I gave an inquiry-based talk on a novel way of approximating e for the Saturday Morning Math Group (SMMG) at UT Austin in Spring 2020. This talk is supplemented by a worksheet, with the accompanying answer key.
- Building Better Teachers: Using Role-play to Create Content Experts (pdf version here). I gave a talk on my experience teaching M371E for the 2020 FIC Graduate Teaching Showcase. You can watch the talk here.
- Ideas and Strategies for Teaching Inclusively and Equitably Online (pdf version here). I gave a talk for the Inequity in STEM Seminar in Summer 2020.
- LaTeX Workshop - CVs, Cover Letters, and SOPs (pdf version here). I gave a talk for MoCAT in Fall 2020.
- What is Algebraic Topology?. I gave a talk for Rose-Hulman in Spring 2021.
- What's it like being a mathematician? (pdf version here). I gave a talk for Connected Research at UCLA in Winter 2022.

## DRP Notes

- DRP notes on Classifying Spaces and Homotopy Theory. These are notes on an inquiry-based DRP project done with Michael Zamora at UT Austin in Fall 2019, supplementing his class in algebraic topology.