Pablo Pelaez  UNAM, Mexico
Talk 1 Title: The slice filtration in motivic homotopy theory.
Abstract: We will discuss several aspects of the slice filtration in motivic homotopy theory.

Pablo Pelaez UNAM, Mexico
Talk 2 Title: Towards a motivic spectral sequence for Quillen Ktheory over nonreduced and singular schemes.
Abstract: We will describe the construction of a spectral sequence converging to the Quillen Ktheory of any scheme of finite type over a field.

Marco Schlichting  University of Warwick Title: Homology stability for SL_n and Euler classes of projective modules
Abstract:
In this talk I will show that for a local ring R with infinite residue field, the relative homology groups
H_i(SLnR,SL_{n1}R) vanish for i less than n and equal to MilnorWitt Ktheory of R for i=n.
If time permits, I will indicate how this leads to a generalization of a theorem of Morel on Euler classes of projective modules.

Wilberd van der Kallen  University of Utrecht Title: Extrapolating an Euler class.
Abstract: Let $R$ be a noetherian ring of dimension $d$ and let $n$ be an integer so that $n\leq d\leq 2n3$.
Let $(a_1,\dots,a_{n+1})$ be a unimodular row so that the ideal $J=(a_1,\dots,a_n)$ has height $n$.
Jean Fasel has associated to this row an element $[(J,\omega_J)]$ in the Euler class group $E^n(R)$,
with $\omega_J:(R/J)^n\to J/J^2$ given by $(\bar a_1,\dots,\bar a_{n1},\bar a_n\bar a_{n+1})$.
If $R$ contains an infinite field $F$ then we show that the rule of Fasel defines a homomorphism
from $\WMS_{n+1}(R)=\Um_{n+1}(R)/E_{n+1}(R)$ to $E^n(R)$. The main problem is to get a well
defined map on all of $\Um_{n+1}(R)$. Similar results have been obtained by
Das and Zinna \cite{DasZinna}, with a different proof.
Our proof uses that every Zariski open subset of $\SL_{n+1}(F)$
is path connected for walks made up of elementary matrices.

Kirsten Wickelgren  Georgia Tech Title: Motivic desuspension
Abstract: This talk will present an EHP sequence in A^1 algebraic topology at p=2, encoding the obstruction to simplicial desuspension. We will discuss a computation and equivariant analogues. This is joint work with Ben Williams, and includes joint work with Aravind Asok and Jean Fasel.
