1.

Record Nr.

UNISALENTO991002954139707536

Autore

Alonso-Gutiérrez, David

Titolo

Approaching the Kannan-Lovász-Simonovits and variance conjectures / David Alonso-Gutiérrez, Jesús Bastero

Pubbl/distr/stampa

Cham : Springer, 2015

ISBN

9783319132624

Descrizione fisica

x, 148 p. ; 24 cm

Collana

Lecture notes in mathematics, 0075-8434 ; 2131

Classificazione

AMS 46-02

AMS 28A

AMS 46B25

AMS 52A22

AMS 60D05

Altri autori (Persone)

Bastero, Jesúsauthor

Disciplina

515.1

Soggetti

Functional analysis

Geometric analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index

Nota di contenuto

The conjectures ; Main examples ; Relating the conjectures ; Appendix ; Index

Sommario/riassunto

Focusing on two central conjectures from the field of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the topics treated. Employing a style suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, allowing readers to quickly access the core of these conjectures. In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan?s work on the connection between the thin-shell



width and the KLS conjecture