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HARMONIC SIGNED

Discrete harmonic analysis for computer science

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EC-Contrib. €

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Project "HARMONIC" data sheet

The following table provides information about the project.

Coordinator
TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY 

Organization address
address: SENATE BUILDING TECHNION CITY
city: HAIFA
postcode: 32000
website: www.technion.ac.il

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Total cost 1˙473˙750 €
 EC max contribution 1˙473˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-STG
 Funding Scheme ERC-STG
 Starting year 2019
 Duration (year-month-day) from 2019-03-01   to  2024-02-29

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY IL (HAIFA) coordinator 1˙473˙750.00

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 Project objective

Boolean function analysis is a topic of research at the heart of theoretical computer science. It studies functions on n input bits (for example, functions computed by Boolean circuits) from a spectral perspective, by treating them as real-valued functions on the group Z_2^n, and using techniques from Fourier and functional analysis. Boolean function analysis has been applied to a wide variety of areas within theoretical computer science, including hardness of approximation, learning theory, coding theory, and quantum complexity theory.

Despite its immense usefulness, Boolean function analysis has limited scope, since it is only appropriate for studying functions on {0,1}^n (a domain known as the Boolean hypercube). Discrete harmonic analysis is the study of functions on domains possessing richer algebraic structure such as the symmetric group (the group of all permutations), using techniques from representation theory and Sperner theory. The considerable success of Boolean function analysis suggests that discrete harmonic analysis could likewise play a central role in theoretical computer science.

The goal of this proposal is to systematically develop discrete harmonic analysis on a broad variety of domains, with an eye toward applications in several areas of theoretical computer science. We will generalize classical results of Boolean function analysis beyond the Boolean hypercube, to domains such as finite groups, association schemes (a generalization of finite groups), the quantum analog of the Boolean hypercube, and high-dimensional expanders (high-dimensional analogs of expander graphs). Potential applications include a quantum PCP theorem and two outstanding open questions in hardness of approximation: the Unique Games Conjecture and the Sliding Scale Conjecture. Beyond these concrete applications, we expect that the fundamental results we prove will have many other applications that are hard to predict in advance.

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