$A^1$-Homotopy Theory and Its Recent Developments

There was a small program during the second term (spring) of the 2009-2010 year on $A^1$-Homotopy Theory and its recent developments. Two directions were 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 $A^1$-homotopy to the study of smooth proper varieties over a field, especially those which are involving the $A^1$-fundamental group of $A^1$-connected varieties.