The motivic Lambda algebra and some applications

Dominic Culver (MPIM Bonn)

Monday 22nd November 16:00-17:00 Online

Abstract

One of the fundamental objects in homotopy theory is the stable homotopy groups of spheres. Several different approaches have been developed to calculate these groups, most notably the Adams spectral sequence. This is a device whose input is algebraic (Ext groups over the Steenrod algebra) and whose output are homotopy groups. Unfortunately, the input, while algebraic, is still incredibly complicated. The Lambda algebra is a convenient DGA whose cohomology is the input to the Adams spectral sequence and has found many interesting applications in homotopy. 

 
On the other hand, Voevodsky has developed motivic homotopy theory, the homotopy theory of schemes. Exactly as in the topological case, there are stable homotopy groups and a motivic Adams spectral sequence. In this talk, I will describe some in which I and my collaborators develop the motivic analogue of the Lambda algebra. Time permitting, I will describe how we can use this algebra to compute an infinite number of d_2-differentials in the motivic Adams spectral sequence over the real numbers.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/98078798957 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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