David McKinnon, Department of Pure Mathematics, University of Waterloo
“Integral points on punctured varieties”
What is an integral point, really? Turns out theres a natural characterisation in terms of schemes (dont worry, Ill be gentle), and theres a natural generalization that appears once you look at the question scheme-theoretically. We all know that integral points are much less common than rational ones, normally, but in this generalized world, that may not always be the case. Ill give a general overview of the situation and describe a question of Brendan Hassett and Yuri Tschinkel. I will then explain how Yongqiang Zhao and I kicked this problems bum and tried to take its name, only to find that Torsten Ekedahl had already taken it. I will then explain how we left Ekedahl in the dust anyway, and proved the most amazing theorems ever, in the history of the world. Um. On this particular problem.
Please note new room.