Unlikely intersections and Chabauty's method

Location: N3.12 (Quillen room).

Time: Wednesdays 13:00-15:00, starting week 2 (Wednesday 23rd October).

Provisional schedule:

• Week 2 (23/10): Chabauty's method. Speaker: Netan

• Week 3 (30/10): Ax-Schanuel and Chabauty over number fields. Speaker: Martin

• Week 4 (6/11): Manin-Mumford and Pila-Zannier. Speaker: Chris?

• Week 5 (13/11): Coleman's proof of Manin-Mumford

• Week 6 (20/11): Ax-Schanuel via o-minimality

• Weeks 7-8 (27/11 and 4/12): Ax-Schanuel for variations of Hodge structure

References:

• "The method of Chabauty and Coleman", McCallum and Poonen, 2012.

• "Effective Chabauty", Coleman, 1985.

• "On Schanuel's conjectures", Ax, 1971.

• "Some Topics in Differential Algebraic Geometry I: Analytic Subgroups of Algebraic Groups", Ax, 1972.

• "Rational points in periodic analytic sets and the Manin-Mumford conjecture", Pila and Zannier, 2008.

• "O-minimality and Diophantine Geometry", eds. Jones and Wilkie, 2015.

• "Ramified torsion points on curves", Coleman, 1987.

• "Ax-Schanuel for Shimura varieties", Mok, Pila and Tsimerman, 2009.

• "The Ax-Schanuel conjecture for variations of Hodge structures", Bakker and Tsimerman, 2019.

• "Hodge loci and atypical intersections: conjectures", Klingler, 2017.