# Talbot 2014: Motivic Homotopy Theory

## Mentored by Marc Levine and Bradley Drew

###
March 16-22, 2014

Pigeon Forge, Tennessee

**Here is a PDF of the syllabus for the 2014 Talbot workshop** (subject to change). This includes detailed talk descriptions and references.

Northwestern University has been conducting a seminar in preparation for the Talbot workshop. Here is the seminar website, which will include some notes once the seminar gets going.

The MIT pre-Talbot seminar webpage can be found here, although its audience is smaller and its schedule less ambitious than its Northwestern counterpart.

The talk schedule is as follows.

#### Monday:

**Introduction and overview**, by Brad Drew and Marc Levine (Duisburg-Essen). Amelia's notes.

**Model categories**, by Vivian Bailey (UCLA). Amelia's notes.

**Quasicategories**, by Meng Guo (Harvard). Amelia's notes.

**Basic constructions with quasicategories**, by Michael Catanzaro (Wayne State). Amelia's notes.

**Localization and the unstable motivic $(\infty, 1)$-category**, by Jay Shah (MIT). Amelia's notes.

#### Tuesday:

**Symmetric monoidal $(\infty,1)$-categories and the stable motivic $(\infty, 1)$-category**, by Amelia Perry (MIT). Amelia's notes.

**Symmetric spectra**, by Irina Bobkova (Northwestern). Amelia's notes.

**Etale classifying spaces and representability of algebraic K-theory**, by Paul VanKoughnett (Northwestern). Paul's notes, Amelia's notes.

**The purity theorem and consequences**, by Marc Hoyois (Northwestern). Amelia's notes.

#### Wednesday:

**Morel's $\A^1$-connectivity theorem and homotopy t-structures**, by Florian Strunk (Regensburg). Amelia's notes.

**Endmorphisms of the sphere spectrum**, by David Yang (MIT). Amelia's notes.

**Introduction to algebraic cobordism and oriented theories**, by Adeel Khan (Duisburg-Essen). Amelia's notes.

**Conference hike.**

#### Thursday:

**Universality of MGL**, by Ben Knudsen (Northwestern). Amelia's notes.

**Landweber exactness**, by Marc Levine (Duisburg-Essen). Amelia's notes.

**The slices of a Landweber exact theory**, by Lorenzo Mantovani (Duisburg-Essen). Amelia's notes.

**Stable homotopy groups of spheres and their motivic analogue over $\operatorname{Spec}(\C)$**, by Zhouli Xu (Chicago). Amelia's notes.

#### Friday:

**The theorem of Hopkins-Morel, Part I**, by Lukas Brantner (Harvard). Lukas's notes.

**The theorem of Hopkins-Morel, Part II**, by David White (Wesleyan). Amelia's notes.

**The theorem of Hopkins-Morel, Part III**, by Dylan Wilson (Northwestern). Amelia's notes.

**Geometric aspects of algebraic cobordism**, by Brian Hwang (Caltech). Amelia's notes.

**Future directions and discussion session**, by Brad Drew and Marc Levine (Duisburg-Essen). Amelia's notes.