A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions

Anindya De
Institute for Advanced Study; Member, School of Mathematics
May 13, 2014
In this talk, we will continue, the proof of the Central Limit theorem from my last talk. We will show that that the law of "eigenregular" Gaussian polynomials is close to a Gaussian. The proof will be based on Stein's method and will be dependent on using techniques from Malliavin calculus. We will also describe a new decomposition lemma for polynomials which says that any polynomial can be written as a function of small number of eigenregular polynomials. The techniques in the lemma are likely to be of independent interest. Based on joint work with Rocco Servedio.

Toy Models

Tadashi Tokieda
Director of Studies in Mathematics, Trinity Hall, University of Cambridge; Radcliffe Fellow, Harvard University
May 16, 2014
Do you want to come see some toys?

"Toy" here has a special sense: an object of everyday life which can be found or made in minutes, yet which, if played with imaginatively, reveals a behavior that sets mathematicians and physicists thinking for days. In this show, Tadashi will perform table-top demos of several such toys and explore the mathematics and physics that open up from them. Some of the toys will be well known but revisited afresh, some will be original, and all will be, it is hoped, entertaining.