SMS scnews item created by Jonathan Hillman at Mon 8 Mar 2010 0852
Type: Seminar
Distribution: World
Expiry: 12 Mar 2010
Calendar1: 12 Mar 2010 1400-1500
CalLoc1: Carslaw 175

Joint Colloquium: Dimca -- From Lang’s conjecture to Torelli groups

Alex Dimca is now at the University of Nice. 
(Many would remember him as a colleague at Sydney in the early 1990s!)

 From Lang’s Conjecture to finiteness properties of Torelli groups


 First we recall one of Lang’s conjectures in diophantine geometry
 on the interplay between subvarieties and translated subgroups in a
 commutative algebraic group
 (proved by M. Laurent in the case of affine tori in 1984).

 Then we present the technique of resonance and characteristic varieties,
 a powerful tool in the study of fundamental groups of algebraic varieties.

 Finally, using the two ingredients above, we show that the Torelli
 groups $T_g$
 have some surprising finiteness properties for $g>3$.
 In particular, we show that for any subgroup $N$ in $T_g$ containing
 the Johnson kernel $K_g$, the complex vector space $N_{ab} \otimes C$
 is finite dimensional.

 All the details are available in our joint preprint with S. Papadima

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