Media

Videos & Notes.

Videos

2026

∞-categories — mini-course (Summer School on Homotopy Colimits, Regina)

2026

Computing persistent homology revisited, revisited (ICERM)

2026

Categorical approach to modularity (NITMB)

2025

An invitation to discrete homotopy theory (AATRN Network Seminar)

2025

Invitation to discrete homotopy theory (Brown CS Theory Seminar)

2023

Calculus of Fractions for Quasicategories (NYU Abu Dhabi)

2023

Higher-dimensional calculus of fractions (Topos Institute)

2021

Cubical setting for Discrete Homotopy Theory (Topos Institute Colloquium)

2020

Cubical models of (∞,1)-categories (Purdue Topology Seminar)

2020

Homotopy Type Theory and Internal Languages of Higher Categories (MSRI)

2020

Homotopy coherent nerve and straightening, cubically (MSRI)

2020

Introduction to Cubical Sets (MSRI)

2017

Type Theory and Higher Categories (Isaac Newton Institute)

2014

Type Theory and Locally Cartesian Closed Quasicategories (HoTT Workshop, Oxford)

2012

The Simplicial Model of Univalence (Institute for Advanced Study)


Notes

2018

Applying for academic jobs in North America (slides)

2017

Diversity in Homotopy Type Theory (with D. Christensen, D. Licata, E. Riehl, M. Shulman)

2013

Introduction to Test Categories (notes from M. Zawadowski's talk)

2011

Fiber Bundles and Univalence (notes from I. Moerdijk's talk, MAP 2011)

2011

The Univalence Axiom and Functional Extensionality (notes from N. Gambino's talk, Oberwolfach)