15:00 - 16:00: Seminar talk

16:00 - 17:00: Panel discussion

Abstract: Arithmetic geometry is at the core of pure mathematics but modern advances in computing power and algorithms are changing the field. I will focus on recent results of the Simons Collaboration "Arithmetic geometry, number theory, and computation". Massive parallel computations are now routinely used to construct large data sets and solve long-standing open problems. Examples include breakthroughs on representing integers as sums of three cubes; the construction of collections of small-genus curves, abelian varieties, and finite groups on the L-functions and Modular Forms Database; and the use of delicate floating point computations to rigorously compute algebraic integers and related invariants.
 
*The lecture will be followed by a panel discussion on the future of extensive computation in sciences (4-5 pm).