|Date||Sept. 2, 2011|
|Speaker||Andrew V. Sutherland (Massachusetts Institute of Technology)|
|Topic||Telescopes for Mathematicians|
|Abstract:|| High performance computing is changing the way mathematicians go about their research. Thanks to cheap parallelism and dramatically faster algorithms, we are now able to “see” objects that were once thought to be computationally inaccessible, and at a remarkable level of detail. This additional resolution allows us to formulate very precise conjectures, and, in many cases, may illuminate the path to a proof.
I will give an overview of some very recent (and still ongoing) research in number theory, concerning analogues of the Sato-Tate conjecture in higher dimension. These conjectures predict the asymptotic behavior of certain arithmetic statistics attached to algebriac curves (and abelian varieties) using a random matrix model. Such models have been used on a heuristic basis for quite some time, but it is only very recently that we have begun, in certain cases, to be able to prove that these models are correct.
My talk will focus on the computational challanges we face in this research, and describe some of the solutions we have obtained thus far. I will also show many of the beautiful pictures (and even videos) that we were able to make with the “telescope” that we built.