This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop "Geometric and Ergodic Aspects of Group Actions," organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and providing clear, detailed accounts of various topics at the interface of ergodic theory, the theory of homogeneous dynamics, and the geometry of hyperbolic surfaces, the book is a valuable resource for researchers and advanced graduate students in mathematics.

Autorentext

S.G. Dani has been a distinguished Professor at the Centre for Excellence in Basic Sciences at the University of Mumbai and the Department of Atomic Energy, Mumbai, India, since July 2017, following an illustrious career at the Tata Institute of Fundamental Research (TIFR), Mumbai, from 1969 to 2012. He has made significant contributions in many areas of mathematics, including ergodic theory, dynamics, number theory, Lie groups, and measures on groups, and has published in many leading international journals. He also has written on the history of mathematics, in ancient as well as recent times in India.

A recipient of the Shanti Swarup Bhatnagar Prize, the Srinivasa Ramanujan Medal, and the Mathematical Sciences Prize of TWAS by the Academy of Sciences of the Developing World, Professor Dani is a Fellow of TWAS and the three major academies of science in India (INSA, IASc, and NASI) and served on the councils of INSA and IASc. He was an invited speaker at ICM 1994. He has been on the editorial boards of several international journals and was the editor of the Proceedings Mathematical Sciences from 1987 to 2000. He is currently the editor of Ganita Bharati and the Bulletin of the Indian Society for History of Mathematics. He was a member of the National Board of Higher Mathematics from 1996 to 2015 and its chairman from 2006 to 2011. He was also the president of the Commission for Development and Exchange of the International Mathematical Union from 2007 to 2010 and is currently a member of the executive committee of the International Commission for History of Mathematics (ICHM). He also is the president of the recently founded Mathematics Teachers' Association, India.

Anish Ghosh is Associate Professor at the School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India. Earlier, he was a lecturer at the University of East Anglia, UK; a research fellow at the University of Bristol, UK; and an instructor at the University of Texas at Austin, USA. He earned his Ph.D. from Brandeis University, USA, in 2006. He has co-edited a book on Recent Trends in Ergodic Theory and Dynamical Systems and published over 36 research articles in several respected international journals. His research interests include the ergodic theory of group actions on homogeneous spaces and interactions with number theory. He is a Fellow of the Indian Academy of Sciences. He won the NASISCOPUS young scientist award 2017 and is a recipient of the Swarnajayanti Fellowship 2017.

Inhalt

1. Lectures on Kleinian Groups.- 2. Horocycle Flows on Surfaces with Infinite Genus.- 3. Higher-Order Correlations for Group Actions.- 4. Exponential Mixing.