[Crib-list] SPEAKER: Andrew V. Sutherland (MIT) -- Computational Research in Boston and Beyond Seminar (CRIBB) -- Friday, Sept. 2, 2011 --12:30 PM in Room 32-124

[Shirley Entzminger]

 	     COMPUTATIONAL RESEARCH in BOSTON and BEYOND SEMINAR


DATE:		Friday, September 2, 2011

TIME:		12:30 PM

LOCATION:	Building 32, Room 124 (Stata Center)
 		(32 Vassar Street, Cambridge)


[Pizza and beverages will be provided at 12:15 PM outside Room 32-124.]


TITLE: 		"Telescopes for Mathematicians"

SPEAKER:	Andrew V. Sutherland  (MIT)


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.

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Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA