GEOMETRY, GROUPS AND DYNAMICS. VOLUME: 639

This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy.
Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Readership
Graduate students and research mathematicians interested in geometry group theory and related areas.

Authors
C. S. Aravinda, TIFR, Bangalore, India.
William M. Goldman, University of Maryland, College Park, MD.
Krishnendu Gongopadhyay, Indian Institute of Science Education and Research Mohali, Punjab, India.
Alexander Lubotzky, Hebrew University of Jerusalem, Israel.
Mahan Mj, RKM Vivekanada University, Howrah, India.
Anthony Weaver, Bronx Community College, CUNY, New York, NY

Contents
Foreword ix
Preface xi

Lecture Notes
Complex Kleinian groups
W. Barrera, A. Cano, J. P. Navarrete, and J. Seade 1
Complete Lorentzian 3-manifolds
Virginie Charette and Todd A. Drumm 43
The Goldman bracket and the intersection of curves on surfaces
Moira Chas 73
An introduction to flows on homogeneous spaces
S. G. Dani 85
Quantitative geometry of hyperbolic manifolds
Peter B. Shalen 103
Discrete groups and Riemann surfaces
Anthony Weaver 129

Research Expositions
A note on Chern’s theorem on invariant measures
Vikram T. Aithal 161
Random affine lattices
Jayadev S. Athreya 169
Upper central series for the group of unitriangular automorphisms of a free associative algebra
Valeriy G. Bardakov and Mikhail V. Neshchadim 175
Hermitian structure and bundles on G/G
Indranil Biswas 189
Log-Riemann surfaces, Caratheodory convergence and Euler’s formula
Kingshook Biswas and Ricardo Perez-Marco 197
Uniformization of simply connected finite type Log-Riemann surfaces
Kingshook Biswas and Ricardo Perez-Marco 205
The Euler characteristic of a Haken 4-manifold
Allan L. Edmonds 217
A discreteness criterion for groups containing parabolic isometries
Viveka Erlandsson and Saeed Zakeri 235
On the z-classes in a centrally finite division ring
Rony Gouraige 243
On Lorentz spacetimes of constant curvature
François Guéritaud 253
On the asymptotic behavior of complex earthquakes and Teichmüller disks
Subhojoy Gupta 271
Characteristically simple Beauville groups, I: Cartesian powers of alternating groups
Gareth A. Jones 289
Relatively hyperbolic spaces
Abhijit Pal and Akshay Kumar Singh 307
Complex hyperbolic free groups with many parabolic elements
John R. Parker and Pierre Will 327
On Fatou components and omitted values
Tarakanta Nayak 349
Some dynamical properties of certain meromorphic functions
Shenglan Yuan 359