Title	Boolean functions, hyperplane arrangements, and random tensors
Creator	Vershynin, Roman
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-03-27T13:52
Description	A simple way to generate a Boolean function in n variables is to take the sign of some polynomial. Such functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? This problem was solved for degree $d=1$ by Zuev in 1989 and has remained open for any higher degrees, including $d=2$, since then. In a joint work with Pierre Baldi (UCI), we settle the problem for all degrees $d>1.$ The solution explores connections of Boolean functions to additive combinatorics and high-dimensional probability. This leads to a program of extending random matrix theory to random tensors, which is mostly an uncharted territory at present.
Extent	35 minutes
Subject	Mathematics; Functional analysis; Convex and discrete geometry
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: University of Michigan
Series	BIRS Workshop Lecture Videos (Banff, Alta)
Date Available	2018-09-24
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0372141
URI	http://hdl.handle.net/2429/67236
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Researcher
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos