Unlikely intersections study group

Jan-March 2018, UCL

Wednesdays 2.00 - 3.30 pm, room 505, UCL maths department (10 January - 21 March)

The aim of the study group is to understand recent progress on unlikely intersections in Shimura varieties, following the strategy of Pila and Zannier using o-minimality. The following themes will appear, each in the context of several different results:

The study group will focus on the case of Shimura varieties, in particular products of modular curves (Y(1)n) and the moduli space of principally polarised abelian varieties (Ag). As it is possible to define these moduli spaces concretely, familiarity with the general theory of Shimura varieties should not be required. We will also discuss abelian varieties (the Manin-Mumford conjecture) as a warm-up, and there will be a talk on results on families of abelian varieties (which can be interpreted as mixed Shimura varieties).


10 Jan Introduction Andrei Yafaev Notes by Gregorio
17 Jan Manin-Mumford conjecture following Pila and Zannier Michele Giacomini Notes by Gregorio
24 Jan André-Oort conjecture for Y(1)n (Pila) Domenico Valloni Notes by Domenico
31 Jan Ax-Lindemann-Weierstrass theorem for Ag (Pila-Tsimerman) Andrei Yafaev Notes by Gregorio
7 Feb Heights of abelian varieties Netan Dogra Notes by Gregorio
14 Feb André-Oort conjecture for Ag (Pila-Tsimerman, Ullmo, Tsimerman) Gregorio Baldi Notes by Gregorio
21 Feb Masser-Wüstholz isogeny theorem Martin Orr Notes by Gregorio
28 Feb Families of abelian varieties (Masser-Zannier, Barroero-Capuano) Laura Capuano
7 Mar No talk
14 Mar André-Pink conjecture (Orr) Domenico Valloni Notes by Gregorio
21 Mar The Colmez conjecture Martin Orr Notes by Gregorio

More detailed draft programme