{"product_id":"dynamics-geometry-number-theory-9780226804026","title":"Dynamics Geometry Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis 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 sectionsArithmeticity, Superrigidity, Normal Subgroups; Discrete Subgroups; Expanders, Representations, Spectral Theory; and Homogeneous Dynamicsthe chapters have all been written by the foremost experts on each topic with a view to making them accessible both\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Margulis is without a doubt one of the most influential mathematicians of the past fifty years. The book \u003ci\u003eDynamics, Geometry, Number Theory\u003c\/i\u003e 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.\" * MAA Reviews *\u003cbr\u003e\"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. \u003ci\u003eDynamics, Geometry, Number Theory\u003c\/i\u003e provides one remedy to that challenge.\" * zbMath *\u003cbr\u003e“Margulis is one of the great mathematicians of the twentieth century and the first decades of this century, whose work is central today. This valuable book collects reflections on his work by some of the most prominent scholars in the area. Uniquely broad in scope, the whole collection is very strong, and the whole is greater than the parts. Terrific!” -- Shmuel Weinberger, University of Chicago\u003cbr\u003e“A superb contribution in every regard: purely scientifically; expounding upon the many deep works of Margulis and thereby appropriately honoring him and his work; and putting the contributions in context and sorting them in appropriate categories, while explaining the deep connections between them. The intellectual level of this book is astounding. I will recommend it to all my associates, graduate students, postdocs, and other researchers, and surely to my library.” -- Ralf Spatzier, University of Michigan\u003cbr\u003e“Margulis’s work has had a tremendous impact on mathematics, and this book will be read by scholars from a broad cross-section of mathematical backgrounds connected to the four sections of the volume and beyond. It will serve as a go-to collection for specialists and graduate students alike.” -- Alan Reid, Rice University\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction\u003cbr\u003e\u003ci\u003eDavid Fisher\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePART I || \u003c\/b\u003e\u003ci\u003eArithmeticity, superrigidity, normal subgroups\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e1. \u003c\/b\u003eSuperrigidity, arithmeticity, normal subgroups: results, ramifications, and directions \u003cbr\u003e\u003ci\u003eDavid Fisher\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e2. \u003c\/b\u003eAn extension of Margulis’s superrigidity theorem\u003cbr\u003e\u003ci\u003eUri Bader and Alex Furman\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e3. \u003c\/b\u003eThe normal subgroup theorem through measure rigidity\u003cbr\u003e\u003ci\u003eAaron Brown, Federico Rodriguez Hertz, and Zhiren Wang\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePART II || \u003c\/b\u003e\u003ci\u003eDiscrete subgroups\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e4. \u003c\/b\u003eProper actions of discrete subgroups of affine transformations\u003cbr\u003e\u003ci\u003eJeffrey Danciger, Todd A. Drumm, William M. Goldman, \u003c\/i\u003e\u003ci\u003eand Ilia Smilga\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e5. \u003c\/b\u003eMaximal subgroups of countable groups: a survey\u003cbr\u003e\u003ci\u003eTsachik Gelander, Yair Glasner, and Gregory Soifer\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePART III || \u003c\/b\u003e\u003ci\u003eExpanders, representations, spectral theory\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e6. \u003c\/b\u003eTempered homogeneous spaces II\u003cbr\u003e\u003ci\u003eYves Benoist and Toshiyuki Kobayashi\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e7. \u003c\/b\u003eExpansion in simple groups\u003cbr\u003e\u003ci\u003eEmmanuel Breuillard and Alexander Lubotzky\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e8. \u003c\/b\u003eElements of a metric spectral theory\u003cbr\u003e\u003ci\u003eAnders Karlsson\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePART IV || \u003c\/b\u003e\u003ci\u003eHomogeneous dynamics\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003e9. \u003c\/b\u003eQuantitative nondivergence and Diophantine approximation on manifolds \u003cbr\u003e\u003ci\u003eVictor Beresnevich and Dmitry Kleinbock\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e10. \u003c\/b\u003eMargulis functions and their applications\u003cbr\u003e\u003ci\u003eAlex Eskin and Shahar Mozes\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e11. \u003c\/b\u003eRecent progress on rigidity properties of higher rank diagonalizable actions and applications\u003cbr\u003e\u003ci\u003eElon Lindenstrauss\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e12. \u003c\/b\u003eEffective arguments in unipotent dynamics\u003cbr\u003e\u003ci\u003eManfred Einsiedler and Amir Mohammadi\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e13. \u003c\/b\u003eEffective equidistribution of closed hyperbolic subspaces in congruence quotients of hyperbolic spaces\u003cbr\u003e\u003ci\u003eManfred Einsiedler and Philipp Wirth\u003c\/i\u003e\u003cbr\u003e\u003cb\u003e14. \u003c\/b\u003eDynamics for discrete subgroups of SL2(C)\u003cbr\u003e\u003ci\u003eHee Oh\u003c\/i\u003e\u003cbr\u003e  \u003c\/p\u003e","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":49400122900823,"sku":"9780226804026","price":61.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226804026.jpg?v=1730469800","url":"https:\/\/bookcurl.com\/products\/dynamics-geometry-number-theory-9780226804026","provider":"Book Curl","version":"1.0","type":"link"}