Abstract: In this talk we present a new proof of the André-Oort conjecture under the Generalised Riemann Hypothesis. In this proof, we generalise the strategy pioneered by Edixhoven, and implemented by Klingler and Yafaev, to all special subvarieties. Thus, we remove ergodic theory from the proof of Klingler, Ullmo and Yafaev and replace it with simple tools from group theory and algebraic geometry. Our key ingredient is a lower bound for the degrees of strongly special subvarieties derived from Prasad’s volume formula for S-arithmetic quotients of semisimple groups.
The seminar is preceded by the Study Group, which will be on aspects of the Geometric Langlands programme, and which is being organized by Alex Paulin.