Algebraic K-theory of quasi-smooth blow-ups and cdh descent
Damien Calaque on Factorization Algebras and Centralizers
Ieke Moerdijk on ∞-categories and ∞-operads
David Ayala: Higher categories are sheaves on manifolds
Lie Algebras and Homotopy Theory (Lurie)
Lurie: "Categorification of the Fourier Transform"
Mini seminar on factorization homology
Lectures on Factorization Homology, Infinity-Categories, and Topological Field Theories
Krause, Nikolaus
course on topological cyclic homology
Lurie:
Rotation Invariance in Algebraic K-theory
Foling Zou on
nonabelian Poincare duality theorem in equivariant factorization homology
Characteristic classes mini-course
by Arun Debray
Stratified spaces:
Clark Barwick - 2/3 Exodromy for ℓ-adic Sheaves
Stefan Schwede:
Global homotopy theory course
Workshop on "∞-categories and their applications"
Tangent ∞-categories and Goodwillie calculus
Workshop videos:
Infinity-Categories, Infinity-Operads, and their Applications
Omar Antolín Camarena
Thom ring spectra and orientation
Claudia Scheimbauer
Dualizability in the factorization higher Morita category
Saul Glasman
Some topics in stratified higher category theory
Hongyi Chu
Enriched ∞-operads
Workshop videos:
Equivariant Derived Algebraic Geometry
Clark Barwick
Parametrized higher category theory and parameterized higher algebra
Abstract nonsense
Gepner:
An Introduction to Higher Categorical Algebra
Cisinski explains why everything is enriched in homotopy types
A Liesurely Introduction to Simplicial Sets
Sheaves and Homotopy Theory (Dugger)
,
Hypercovers and simplicial presheaves
A primer on homotopy colimits (Dugger)
Catégories supérieures et théorie des topos (Cisinski)
On Infinity Topoi (Lurie)
Topoi:
Toposes in Como (see Borceux, Lafforgue)
Topos à l'IHES (see Anel, Joyal, Vaquié)
Virtual Workshop on Higher Topos Theory (November 20/21 2020)
Rezk:
Lectures on Higher Topos Theory (Leeds, June 2019)
Rezk:
Toposes and Homotopy Toposes
Category theory:
This is the (co)end, my only (co)friend
Category Theory in Context
Categorical homotopy theory
Elements of ∞-Category Theory
The Formal Theory of Adjunctions Monads Algebras and Descent Emily Riehl MSRI
A short course on ∞-categories (Moritz Groth)
Lax colimits and free fibrations in ∞-category theory
Yonatan Harpaz:
Introduction to stable ∞-categories
Geometry:
The Rising Sea
Notes on algebraic stacks by Anatoly Pregel
Toën
Master course on algebraic stacks
Rezk on spectral algebraic geometry
Structured Spaces (Lurie)
Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi
Derived Algebraic Geometry Winter School 2013
Ben-Zvi on geometric function theory
"Localizations of tensor categories and fiber products of schemes" (cool stuff about quasicoherent sheaves on fibre products)
Omar Antolín Camarena
:
Minicurso de geometría algebraica derivada
Adeel Khan's lecture notes:
Descent in algebraic K-theory
2017/2018
Grothendieck-Riemann-Roch theorem
2018
Descent in algebraic K-theory
2020
Other resource lists:
Tons of references on chromatic homotopy theory and neighbouring topics
Tyler Lawson's reference list for topological modular forms
Doug Ravenel's archive
Videos on Dan Isaksen's Youtube channel