Next Seminar

Large values of the Riemann zeta function in short intervals

Speaker: Louis-Pierre Arguin (New York)

Date: 2020.05.28

Time: 13:00 UTC


In a seminal paper in 2012, Fyodorov & Keating proposed a series of conjectures describing the statistics of large values of zeta in short intervals of the critical line. In particular, they relate these statistics to the ones of log-correlated Gaussian fields. In this lecture, I will present recent results that answer many aspects of these conjectures. Connections to problems in number theory will also be discussed.

Supervised Learning between Function Spaces

Speaker: Andrew Stuart (Caltech)

Date: 2020.05.28

Time: 14:00 UTC


Consider separable Banach spaces X and Y, and equip X with a probability measure m. Let F: X --> Y be an unknown operator. Given data pairs {x_j,F(x_j)} with {x_j} drawn i.i.d. from m, the goal of supervised learning is to approximate F. The proposed approach is motivated by the recent successes of neural networks and deep learning in addressing this problem in settings where X is a finite dimensional Euclidean space and where Y is either a finite dimensional Euclidean space (regression) or a set of finite cardinality (classification). Algorithms which address the problem for infinite dimensional spaces X and Y have the potential to speed-up large-scale computational tasks arising in science and engineering in which F must be evaluated many times. The talk introduces an overarching approach to this problem and describes three distinct methodologies which are built from this approach. Basic theoretical results are explained and numerical results presented for solution operators arising from elliptic PDEs and from the semigroup generated by Burgers equation.

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