Lectures on The interrelation between Hilbert’s Tenth Problem and arithmetic geometry

Lectures 3 & 4 by Carlo 

Thursday 26 June, 10:30-12:00 & 13:00-14:30 

These lectures focus on the use of elliptic curves in proving H10/R for any finitely generated ring R; using many existing reductions, one arrives at a problem of controlling Selmer groups of an analogue of the Manin elliptic curve, which is done by new tools using additive combinatorics.