Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Dominic Culver
Affiliation:

MPIM
Date:

Thu, 02/12/2021 - 15:00 - 16:00 Meeting ID: 931 7291 0947

For passcode please contact Christian Kaiser (kaiser@mpim....)

A longstanding problem in algebraic topology is computing the stable homotopy groups of spheres. A standard tool of the trade is the so called Adams spectral sequence which gives an algebraic approximation to these groups as Ext over a certain algebra. However, even computing this approximation is a difficult task. The Lambda algebra, initially due to Bousfield-Curtis-Kan-Quillen-Rector-Schlesinger, has been used to great effect to better understand this algebraic approximation and the stable homotopy groups themselves.

Motivic homotopy theory, on the other hand, has analogues of many classical objects in algebraic topology. In particular, there are the motivic stable homotopy groups of spheres and a motivic version of the Adams spectral sequence. Unsurprisingly, the motivic approximations are just as, if not more difficult, to compute. In this talk, I will discuss a motivic version of the Lambda algebra and some applications.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/158