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.