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.