Wednesday, 10:00-12:00, Sala Riunioni II floor

The course is devoted to the concept of an infinity
category. In the first session, Rosanna Laking will guide us
through the video of an introductory lecture by Emily Riehl.
Next, we will review the notion of a model category and discuss
some motivating examples from algebraic topology. Then we will
read some chapters of the book "Higher Categories and
Homotopical Algebra" by Denis-Charles Cisinski. Finally, there
will be a lecture series delivered by Gustavo Jasso from the
University of Bonn.

** Start:
Wednesday, November 13.
**

**Program:
**

November 13th: Introduction (Rosanna Laking, video of a
lecture by Emily Riehl)

November 20th: Model Categories, part 1 (Tsutomu Nakamura)

November 27th: Model Categories, part 2 (Francesco
Sentieri)

December 4th** (9:30-11:30): **Model Categories, part 3

**December 9th: ** The Fundamental Groupoid (Sofia
Franchini/Giulia Cavicchioni)

December 11th: Geometric and Combinatorial Simplicies
(Sofia Franchini/Giulia Cavicchioni)

January 8th: The category of
simplicial sets and the nerve of a category (Lidia Angeleri)

January 15th: ∞-categories (Cao Weiqing)

January 29th: Kan-Quillen and Joyal
model structures (Rosanna Laking)

February 5th: Fibrations and
opfibrations (Lorenzo Martini)

February 12th: The Grothendieck construction
(Rosie Laking)

** Lecture Series
by Gustavo Jasso, University of Bonn:
**

Tuesday, February
18, 10:00-12:00

Wednesday, February 19, 11:00-12:00

Thursday, February 20, 10:00-12:00

Tuesday, February
18, and Friday, February 21, 14:00-16:00: Discussion

Allen Hatcher,

Denis-Charles Cisinski,

Michael Barr, Charles Wells

Emily Riehl, The model-independent theory of (∞,1)-categories (lectures at Isaac Newton Institute for Mathematical Sciences 2018; video available on https://www.newton.ac.uk/event/hhhw01/timetable)