## Logistics

• Seminar begins: October 17th, 2017.
• Seminar time: Tuesdays 16:00-18:00
• Seminar location: M101
• George Raptis and I are available by appointment for assisting with talk preparation (we encourage speakers to take advantage of this).
• Detailed list of topics.
• Previous seminars:

## Specialized Plan for the 2017/2018 Winter Semester

This semester we will focus on Goodwillie's functor calculus from an $$\infty$$-categorical viewpoint. As source material we will consider the relevant sections from Lurie's Higher Algebra, as well as more classical sources. We will also consider some applications and examples from the theory.

Our plan will be very roughly guided by the plan of the AG given here.

## General Plan

The purpose of this seminar is to study the general theory of higher categories and its applications. Higher category theory, especially the theory of $$(\infty,n)$$-categories, provides a powerful language for handling the complexity of encoding relations, relations between relations, and "so on".

This language has been applied to questions in homotopy theory, derived algebra, derived algebraic geometry, topological field theory, and computer science. In addition to conceptualizing classical results by placing them in a more general context, they have proven essential for studying homotopy theories themselves.

The exact subject matter of the seminar will be determined by the participants and their interests. In particular, participants are encouraged to speak about related topics arising in recent research papers. We also encourage participants to give talks on various foundational topics including, but not limited to, models for $$(\infty,n)$$-categories, presentable $$\infty$$-categories, higher topoi, stable $$\infty$$-categories, (higher) operad theory, derived schemes, (derived) stacks, the cobordism hypothesis, bicategories, higher Picard and Brauer groups...and beyond!

Participants should have some familiarity with the theory of $$\infty$$-categories.

## Schedule

• 17.10.2017 (Ulrich Bunke) First results in Goodwillie's functor calculus. (Source: HA 6.1.1 through the Statement of 6.1.2.4)
• 24.10.2017 (Justin Noel) Introduction to Goodwillie's functor calculus.
• 31.10.2017 No talk (Vorlesungsfreie Zeit)
• 7.11.2017 (Kim Nguyen) The Taylor tower (Source: HA 6.1.2)
• 14.11.2017 (Matan Prezma) Multivariable calculus (Source: HA 6.1.3)
• 21.11.2017 (Han-Ung Kufner) Symmetric functors (Source: HA 6.1.4)
• 28.11.2017 (Harry Gindi) Norm maps (Source: HA 6.1.6)
• 5.12.2017 (Georgios Raptis) Derivatives of Functors (Source: HA 6.2.1)
• 12.12.2017 (TBD) Parametrized stabilization (Source: HA 6.2.2)
• 19.12.2017 (TBD) Differentials (Source: HA 6.2.3)
• 9.1.2018 (Denis-Charles Cisinski) Derivatives of the identity functor of based spaces (Multiple sources: HA 6.3.3, Brenda Johnson's TAMS paper, Arone-Kankaanrinta, Arone-Mahowald's Inventiones paper, Kuhn's survey) (see this program for detailed references)
• 16.1.2018 (Markus Land) Goodwillie Calculus and Chromatic Homotopy Theory (Source: Kuhn's guide to Telescopic functors)
• 23.1.2018 (TBD) Analyticity and the uniqueness of analytic continuation (Source: Goodwillie Calculus II)
• 30.1.2018 (TBD) Derivatives of A(-) and friends (Source: Goodwillie Calculus I and III)
• 6.2.2018 (TBD) Dundas-Goodwillie-McCarthy (Source: The local structure of algebraic K-theory)