No Where to Go But High: A Perspective on High Dimensional Expanders

04/20/2023
by   Roy Gotlib, et al.
0

"No Where to go but in" is a well known statement of Osho. Osho meant to say that the answers to all our questions should be obtained by looking into ourselves. In a paraphrase to Osho's statement we say "No Where to go but high". This meant to demonstrate that for various seemingly unrelated topics and questions the only way to get significant progress is via the prism of a new philosophy (new field) called high dimensional expansion. In this note we give an introduction [This introduction reflects the authors' interests and by no mean claim to represent the field in a through way] to the high dimensional expansion philosophy, and how it has been useful recently in obtaining progress in various questions in seemingly unrelated fields. This exposition is dedicated to the memory of my mother, Sarah Kaufman, who was always trying to understand the reason why things behave in a certain way. It is also dedicated to the memory of my father Eliezer Kaufman.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/13/2019

A farewell to Professor RNDr. Věra Trnková, DrSc

This is an introduction of the volume of the journal Commentationes Math...
research
03/07/2018

Good Distance Lattices from High Dimensional Expanders

We show a new framework for constructing good distance lattices from hig...
research
11/17/2021

Hypercontractivity on High Dimensional Expanders: Approximate Efron-Stein Decompositions for ε-Product Spaces

We prove hypercontractive inequalities on high dimensional expanders. As...
research
09/13/2023

The Way We Were: Structural Operational Semantics Research in Perspective

This position paper on the (meta-)theory of Structural Operational Seman...
research
08/05/2022

Beyond the Worst Case: Structured Convergence of High Dimensional Random Walks

One of the most important properties of high dimensional expanders is th...
research
08/05/2014

Computing With Contextual Numbers

Self Organizing Map (SOM) has been applied into several classical modeli...
research
06/22/2021

Notes on the H-measure of classifier performance

The H-measure is a classifier performance measure which takes into accou...

Please sign up or login with your details

Forgot password? Click here to reset