Talks

Mini-courses

• The model-independent theory of (∞,1)-categories delivered at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge as part of the workshop Higher structures in homotopy theory to open the semester program Homotopy Harnessing Higher Structures: lecture 1, lecture 2, lecture 3, lecture 4.
• A mini course ∞-category theory from scratch given at the 2015 Young Topologists’ Meeting: lecture 1, lecture 2, lecture 3, lecture 4.

Technical lectures

• A macrocosm principle for cartesian fibrations given at the Workshop on Higher Structures in Geometry and Physics at the Fields Institute.
• A formal theory for ∞-categories, slides from the 2019 International Category Theory Conference in Edinburgh.
• The synthetic approach to ∞-category theory from the Summer School on Higher Topos Theory and Univalent Foundations at Leeds.
• The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories given at the Vladimir Voevodsky Memorial Conference at IAS; slides.
• A proof of the model-independence of ∞-category theory delivered at the workshop ∞-Categories, ∞-Operads, and their Applications at the Casa Matématica Oaxaca.
• A proof of the model-independence of (∞,1)-category theory, slides from a talk given at the 2018 International Category Theory Conference.
• The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories, from the Homotopy Type Theory Electronic Seminar Talks; slides.
• Foundations of (∞,2)-category theory, a talk at the Women in Topology workshop at MSRI outlining a research program.
• Towards a synthetic theory of (∞,1)-categories given at the 2016 Workshop on Homotopy Type Theory and Univalent Foundations of Mathematics at the Fields Institute.
• The formal theory of adjunctions, monads, algebras, and descent, from the workshop Reimagining the Foundations of Algebraic Topology at MSRI; slides.
• Limits of quasi-categories with (co)limits, from the Connections for Women workshop at MSRI.
• Homotopy coherent adjunctions, slides from the AMS Special Session on Homotopy Theory at the 2014 Joint Mathematics Meetings.
• The formal theory of homotopy coherent monads, slides from the Samuel Eilenberg Centenary Conference.

Colloquia

• Elements of ∞-Category Theory, a colloquium hosted by the Matrix Institute; slides.
• Elements of ∞-Category Theory, a virtual talk for the Mathematical Picture Language seminar at Harvard; slides.
• ∞-category theory for undergraduates, a talk in the Berkeley Logic Colloquium; slides.
• The complicial sets model of higher ∞-categories, slides from Structures supérieures at CIRM.
• The complicial sets model of higher ∞-categories slides from Between Topology and Quantum Field Theory: A conference in celebration of Dan Freed’s 60th birthday.
• The complicial sets model of higher ∞-categories, slides from a colloquium given at the Perimeter Institute.
• A universal approach to universal algebra, a colloquium given at the Center for Geometry and Physics in Pohang, Korea.
• Quasi-category theory you can use, slides from the Graduate Student Topology and Geometry Conference at UT Austin.

General audience

• A brief introduction to ∞-cosmoi and higher category theory, filmed by Quanta Magazine.
• A formal language for ∞-category theory, the 2020 President’s Frontier Award lecture.