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 (A_{g}). 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 A_{g} (Pila-Tsimerman) | Andrei Yafaev | Notes by Gregorio |
7 Feb | Heights of abelian varieties | Netan Dogra | Notes by Gregorio |
14 Feb | André-Oort conjecture for A_{g} (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 |