02569nam a2200361 i 4500991002954139707536160726s2015 sz b 001 0 eng d9783319132624b14259746-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.123AMS 46-02AMS 28AAMS 46B25AMS 52A22AMS 60D05Alonso-Gutiérrez, David716387Approaching the Kannan-Lovász-Simonovits and variance conjectures /David Alonso-Gutiérrez, Jesús BasteroCham :Springer,2015x, 148 p. ;24 cmLecture notes in mathematics,0075-8434 ;2131Includes bibliographical references and indexThe conjectures ; Main examples ; Relating the conjectures ; Appendix ; IndexFocusing 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 conjectureFunctional analysisGeometric analysisBastero, Jesúsauthorhttp://id.loc.gov/vocabulary/relators/aut536463.b1425974622-11-1626-07-16991002954139707536LE013 46-XX ALO11 (2015)12013000293738le013pE36.39-l- 01010.i1578884222-11-16Approaching the Kannan-Lovász-Simonovits and variance conjectures1411158UNISALENTOle01326-07-16ma -engsz 00