A1-Homotopy Theory and its Recent Developments

There will be a small program during the second term (spring) of the 2009-2010 year on A¹-Homotopy Theory and its recent developments.  Two directions will be emphasized during this program: the proof of Bloch-Kato conjecture on Galois cohomology and related applications, following the work of Rost and Voevodsky, as well as recent geometric applications of A¹-homotopy to the study of smooth proper varieties over a field, especially those which are involving the A¹-fundamental group of A¹-connected varieties.