This page is for expository notes, slides, and papers. Most of these materials cover topics I am interested in researching, sometimes from a non-standard perspective, but are not based on original work.


  • Test Category Structure of Cube Categories. Cubical Sets Seminar, MSRI, May 2020. [Slides]
  • Types as Weak Omega-Groupoids. School and Workshop on Univalent Foundations, April 2019. [Slides]
  • Comparing Shapes for Higher Structures. Young Topologists Meeting, July 2018. [Slides]
  • Topological Data Analysis. Indian Institute of Science, April 2016. [Slides]
  • Category Theory and Functional Data Abstraction. Brandeis University, May 2015. [Slides]


  • A Brief Tour of Homotopy Type Theory. Cornell Logic Seminar, Spring 2020. [PDF]
  • Simple Homotopy Theory and K1. Fall 2019. [PDF]
  • Topological Modular Forms. Spring 2019. [PDF]
  • Nerves of Higher Categories. Homotopy Group Student Seminar, Spring 2019. [PDF]
  • Homotopy Theory Primer for Type Theory. Homotopy Type Theory Reading Group, Spring 2018. [PDF]
  • Operations Arising from Equivariant K-theory of the Symmetric Group. Fall 2017. [PDF]
  • Summary of Intro Topology and Special Topics. Fall 2015. [PDF]

Course Papers

  • Representability of Homotopy Groups in Type Theory. Cornell University, Fall 2017. [PDF]
  • A Pointless Topological Equivalence. Brandeis University, Fall 2015. [PDF]
  • Category Theory and Functional Data Abstraction. Brandeis University, Spring 2015. [PDF]

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