Jordan Ellenberg, UW Madison

December 11th, 2020 4:00-5:00 pm CET

Title : Some questions around counting rational points on stacks

Abstract : I will talk about a few open questions in arithmetic enumeration which are superficially different but which all arise as special cases of a conjecture of Batyrev-Manin type for algebraic stacks formulated by Matt Satriano, David Zureick-Brown, and me. To state the conjecture precisely requires one to say what one means by the height of a point on a stack; some of you have heard me talk about this part before, so I am going to attempt to abbreviate that story somewhat and use it as a black box, focusing instead on some of the geometric challenges of formulating a counting conjecture, which we have sort of but not fully satisfyingly surmounted.