Dynamics, Geometry, Number Theory

The Impact of Margulis on Modern Mathematics

Inbunden, Engelska, 2022

676 kr

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Beskrivning

This definitive synthesis of mathematician Gregory Margulis’s research brings together leading experts to cover the breadth and diversity of disciplines Margulis’s work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sections—“Arithmeticity, Superrigidity, Normal Subgroups”; “Discrete Subgroups”; “Expanders, Representations, Spectral Theory”; and “Homogeneous Dynamics”—the chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.

Produktinformation

Utgivningsdatum:2022-02-07
Mått:152 x 229 x 43 mm
Vikt:880 g
Format:Inbunden
Språk:Engelska
Antal sidor:496
Förlag:The University of Chicago Press
ISBN:9780226804026

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

David Fisher is the Ruth N. Halls Distinguished Professor of Mathematics at Indiana University, Bloomington. Dmitry Kleinbock is professor of mathematics at Brandeis University. Gregory Soifer is professor emeritus of mathematics at Bar-Ilan University, Israel.

Recensioner i media

"Margulis is without a doubt one of the most influential mathematicians of the past fifty years. The book Dynamics, Geometry, Number Theory is vast in scope and provides an excellent introduction to Margulis's work and the research that it has inspired. It will be of great interest not only to specialists, but to graduate students and researchers interested in ergodic theory, Lie theory, geometry, and number theory."

Innehållsförteckning

IntroductionDavid FisherPART I || Arithmeticity, superrigidity, normal subgroups1. Superrigidity, arithmeticity, normal subgroups: results, ramifications, and directions David Fisher2. An extension of Margulis’s superrigidity theoremUri Bader and Alex Furman3. The normal subgroup theorem through measure rigidityAaron Brown, Federico Rodriguez Hertz, and Zhiren WangPART II || Discrete subgroups4. Proper actions of discrete subgroups of affine transformationsJeffrey Danciger, Todd A. Drumm, William M. Goldman, and Ilia Smilga5. Maximal subgroups of countable groups: a surveyTsachik Gelander, Yair Glasner, and Gregory SoiferPART III || Expanders, representations, spectral theory6. Tempered homogeneous spaces IIYves Benoist and Toshiyuki Kobayashi7. Expansion in simple groupsEmmanuel Breuillard and Alexander Lubotzky8. Elements of a metric spectral theoryAnders KarlssonPART IV || Homogeneous dynamics9. Quantitative nondivergence and Diophantine approximation on manifolds Victor Beresnevich and Dmitry Kleinbock10. Margulis functions and their applicationsAlex Eskin and Shahar Mozes11. Recent progress on rigidity properties of higher rank diagonalizable actions and applicationsElon Lindenstrauss12. Effective arguments in unipotent dynamicsManfred Einsiedler and Amir Mohammadi13. Effective equidistribution of closed hyperbolic subspaces in congruence quotients of hyperbolic spacesManfred Einsiedler and Philipp Wirth14. Dynamics for discrete subgroups of SL2(C)Hee Oh