Dynamics, Geometry, Number Theory

This definitive synthesis of mathematician Gregory Marguliss research brings together leading experts to cover the breadth and diversity of disciplines Marguliss 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 to graduate students and to experts in other parts of mathematics. This was no simple feat: Marguliss 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 Marguliss area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge.