09:00 to 09:55 Registration 09:55 to 10:00 Welcome - David Wallace (INI Director) 10:00 to 11:00 P Deligne ([IAS])Counting l-adic representations, in the function field case We will explain some countings similar to the one Drinfeld did in 1981, and wonder what they mean. INI 1 11:00 to 11:30 Coffee 11:30 to 12:30 On the noncommutative Iwasawa Main Conjecture for CM-elliptic curves We discuss under which assumptions the (commutative) 2-variable Main Conjecture for CM-elliptic curves (due to Rubin, Yager, Katz etc.) implies the non-commutative Main Conjecture as formulated together with Coates, Fukaya, Kato and Sujatha. Related Links •http://www.mathi.uni-heidelberg.de/~otmar/ - personal homepage INI 1 12:30 to 13:30 Lunch at Wolfson Court 14:00 to 15:00 Grothendieck's Section Conjecture and zero-cycles on varieties After some background material on Grothendieck's Section Conjecture, we discuss an obstruction for the existence of splittings of the abelianized homotopy exact sequence for the étale fundamental group. As an application, we explain how to find examples for smooth projective curves over Q that have points everywhere locally but the homotopy exact sequence does not split. This is joint work with David Harari, with explicit examples contributed by Victor Flynn. INI 1 15:00 to 15:30 Tea 15:30 to 16:30 On the p-adic local Langlands correspondence for $GL_2({\bf Q}_p)$ INI 1 16:30 to 17:30 Discussion 17:30 to 18:30 Welcome Wine Reception 18:45 to 19:30 Dinner at Wolfson Court (Residents Only)