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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Applications of Group Cohomology to 3-manifolds. I gave this talk for the junior topology seminar at UT Austin in Spring 2020.
  6. Picard Groups of Stable Module Categories. I gave this talk for the GROOT Summer Seminar online in Summer 2020. Video available here.
  7. 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:
  8. 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.
  9. 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.
  10. 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.
  11. 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

  1. 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.
  2. Modular Representation Theory and Phantom Maps. I gave this talk for the student geometry seminar at UT Austin in Fall 2016.
  3. Taylor Towers and Snaith Splitting. I gave this talk for the homotopy theory student seminar on Goodwillie Calculus at UT Austin in Fall 2017.
  4. 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.
  5. 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.
  6. Picard Groups. I gave this talk for the student geometry seminar at UT Austin in Fall 2018.
  7. Algebraic Methods for Computing Picard Groups. I gave this talk for my oral candidacy exam at UT Austin in Fall 2018.

Expository/Outreach

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. LaTeX Workshop - CVs, Cover Letters, and SOPs (pdf version here). I gave a talk for MoCAT in Fall 2020.
  7. What is Algebraic Topology?. I gave a talk for Rose-Hulman in Spring 2021.
  8. What's it like being a mathematician? (pdf version here). I gave a talk for Connected Research at UCLA in Winter 2022.

DRP Notes

  1. 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.