Programme for Active Period in Arithmetic Geometry
Week 9: Monday 9 – Friday 13 June

Tuesday 10 – Wednesday 11 June, short course
Times and Room: Tuesday and Wednesday 10 – 11 and 12 – 1, MS.04
Speaker: Nils Bruin (Simon Fraser)
Title: Chabauty Methods
Thursday 12 June, seminar
Time and Room: 11 – 12, MS.04
Speaker: Michael Stoll (Jacobs University)
Title: Rational 6-Cycles under Quadratic Maps
Friday 13 June, short course
Times and Room: 11 – 12 and 2 – 3, B3.02
Speaker: Sir Peter Swinnerton-Dyer (Cambridge)
Title: The Manin Conjecture
Friday 13 June, Mathematics Institute Colloquium
Time and Room: 4 – 5, B3.02
Speaker: Bjorn Poonen (Berkeley)
Title: Undecidability in number theory
Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson, showed that no such algorithm exists. But the answer to the analogous question with Z replaced by Q is still unknown, and there is not even agreement among experts as to what the answer should be. I will discuss this and Hilbert's Tenth Problem over other rings of arithmetic interest.