Organized by: Dan Christensen and Chris Kapulkin.
Time: Thursday, 1  2:30 PM.
Location: MC 107.
Date  Speaker  Title and abstract 

September 15th  Chris Kapulkin  Motivation and Basic Concepts I will present the motivation to study higher category theory coming from different areas (homotopy theory, TQFTs, derived algebraic geometry) and introduce basic concepts of quasicategory theory, such as: homotopies and equivalences, proving some of their properties. 
September 22nd  Dan Christensen  The Joyal model structure on simplicial sets I will discuss the class of "weak categorical equivalences" between simplicial sets, which form the weak equivalences in the Joyal model structure, whose fibrant objects are the quasicategories. [notes] 
September 29th  Karol Szumiło  The Joyal model structure on simplicial sets II I will construct the Joyal model structure. 
October 6th  Alex Rolle  Coherent Nerve and Simplicial Localization This talk will introduce two new models of infinity categories (simpliciallyenriched categories and relative categories), and relate them to quasicategories. [notes] 
October 13th  Aji Dhillon  Mapping spaces in higher categories (I) The goal of these two talks is to introduce models for mapping spaces in higher categories and show that they are all equivalent. In the process we will discuss straightening and unstraightening, infinity analogue of the Grothendieck construction. We will conclude with a discussion of cartesian fibrations. [notes] 
October 20th  Aji Dhillon  Mapping spaces in higher categories (II) The goal of these two talks is to introduce models for mapping spaces in higher categories and show that they are all equivalent. In the process we will discuss straightening and unstraightening, infinity analogue of the Grothendieck construction. We will conclude with a discussion of cartesian fibrations. [notes] 
October 27th  Dinesh Valluri  Joins, slices, and limits in quasicategories In this talk we will introduce the notions of join, slice, (co)limits in the context of ∞categories. We will also discuss some basic properties relevant to these constructions. [notes] 
November 3rd  Luis Scoccola  Adjoint functors between quasicategories We will generalize the concept of adjoint functors to the theory of quasicategories. [notes] 
November 10th  Luis Scoccola  Yoneda embedding for quasicategories We will discuss some basic properties of the quasicategory of spaces, presenting in particular the quasicategorical analog of the Yoneda embedding. [notes] 
November 17th  Marco Vergura  Complete Segal Spaces We will introduce Complete Segal spaces and prove they describe an equivalent homotopy theory to the one of quasicategories. [notes] 
November 24th  Marco Vergura  Simplicial and relative categories We describe how simplicial and relative categories form a model of (∞,1)categories. [notes] 
December 1st  James Richardson  Presentable ∞categories I will introduce presentable quasicategories and discuss some of their properties. I will then discuss their relationship with combinatorial model categories. [notes] 
December 8th  Pál Zsámboki  Equivalent notions of ∞topoi Let X be a quasicategory. Then it is an ∞topos, if it is an accessible left exact localization of the presheaf category of a small quasicategory. We will introduce two sets of intrinsic conditions which are equivalent to being an ∞topos:

For more information, contact Chris Kapulkin.
Last updated by Chris Kapulkin on December 16th, 2016.