Seminar: Topics in (∞,2)-categories

During the Summer semester 2023, I’m organizing a seminar on Topics in (∞,2)-categories. We will have an overview of different models of (∞,2)-categories, as well as some constructions thereof, such as the Gray tensor product and (∞,2)-limits. We will also see some applications of (∞,2)-category theory in derived algebraic geometry, topological quantum field theory, and K-theory.

The seminar will take place on Wednesdays from 10:15-11:45 in room M009 and on zoom. Here is a detailed program.

April 192-categories and double categoriesBenedikt Froehlich
April 26(∞,1)-categories and enriched models of (∞,2)-categoriesJana Nickel
May 3Model of complete Segal $\Theta_2$-spacesMarco Giustetto
May 10Models of double ∞-categories and 2-fold complete Segal spacesDivya Ghanshani
May 17Model of scaled simplicial setsJana Nickel
May 24Gray tensor product for 2-categoriesVikram Nadig
May 31Gray tensor product for (∞,2)-categoriesJun Xu
June 7Universal property of the (∞,2)-category of correspondencesJohannes Glossner
June 14Limits in a 2-categoryLyne Moser
June 21The fully extended 2-dimensional cobordism hypothesisPier-Federico Pacchiarotti
June 28Six functor formalismJohannes Glossner
July 5Functoriality of the stable $A_1$-homotopy categoryNiklas Kipp
July 12Limits in an (∞,2)-categoryNima Rasekh
July 19K-theory via double categoriesMaru Sarazola