# Seminars in geometry/topology

## Spring 2013

## Monday March 4, 13:15 - 14:00, room 656, Sentralbygg 2

Truls Bakkejord RĂ¦der: *Hopf algebroids: Part I*

**Abstract:** In this first talk, I will discuss the role Hopf algebras, e.g. the mod 2 Steenrod algebra, play in stable homotopy theory. I will then describe a generalisation of these to Hopf algebroids, and explain why they are useful and why they are a natural concept to study. Roughly speaking, the passage from Hopf algebras to Hopf algebroids is analogous to the passage from groups to groupoids. Finally, I will briefly mention the application of particular Hopf algebroids as E_2-terms of the Adamsâ€”Novikov spectral sequence.

## Friday February 22, 13:15 - 15:00, room 734, Sentralbygg 2

Richard Williamson: *A dream in motivic homotopy theory*

**Abstract:** This is the first in a planned series of topology seminars this
term which will present aspects of the story and motivation
behind our research interests.

I will discuss an idea that I am working on in motivic homotopy theory. Most of the talk will be expository.

We will first discuss the Weil conjectures. The proving of these conjectures in the 1960s-70s represents for me one of the very highest and most profound achievements of mathematics in the twentieth century.

From here we will discuss the idea of a motive, and discuss something of the conjectural picture of the motivic world, touching upon the 'standard conjectures' (which include the Hodge conjecture, one of the seven millenium problems) on which the picture depends.

We will then leap forward to the idea of motivic cohomology. Finally, we will be in a position to explore motivic homotopy theory.