Andrei Yafaev

Lower bounds for Galois orbits of special points and the Andre-Oort conjecture

The Andre-Oort conjecture has been an open problem for over 30 years. The last hurdle in its proof (using the strategy using o-minimality) has been the problem of bounding below the degrees of special points in Shimura varieties. In a joint work with Gal Biniyamini and Harry Schmidt, we have proved the lower bounds conditional on a conjecture on bounds on heights of special points. Very recently J. Pila and J. Tsimerman have announced the proof of this conjecture thus completing the proof. We will present the work with G. Biniyamini and H. Schmidt.