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Computational aspects of discrete subgroups of Lie groups : Virtual Conference Computational Aspects of Discrete Subgroups of Lie Groups, June 14-18, 2021, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island
This volume contains the proceedings of the virtual workshop on Computational Aspects of Discrete Subgroups of Lie Groups, held from June 14 to June 18, 2021, and hosted by the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island.The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representation of groups and their geometric properties. It is centered on computing with discrete subgroups of Lie groups, which impacts many different areas of mathematics such as algebra, geometry, topology, and number theory. The workshop aimed to synergize independent strands in the area of computing with discrete subgroups of Lie groups, to facilitate solution of theoretical problems by means of recent advances in computational algebra.
eBook
Discrete groups and geometric structures : Workshop on Discrete Groups and Geometric Structures, with Applications III, May 26-30, 2008, Kortrijk, Belgium
This volume reports on research related to Discrete Groups and Geometric Structures, as presented during the International Workshop held May 26-30, 2008, in Kortrijk, Belgium. Readers will benefit from impressive survey papers by John R. Parker on methods to construct and study lattices in complex hyperbolic space and by Ursula Hamenstadt on properties of group actions with a rank-one element on proper CAT (0)-spaces. This volume also contains research papers in the area of group actions and geometric structures, including work on loops on a twice punctured torus, the simplicial volume of products and fiber bundles, the homology of Hantzsche - Wendt groups, rigidity of real Bott towers, circles in groups of smooth circle homeomorphisms, and groups generated by spine reflections admitting crooked fundamental domains.
eBook
Geometric algorithms for discreteness and faithfulness
In this paper I describe two geometric algorithms for certifying discreteness and freeness of finitely generated subgroups of
Book Chapter
Combinatorial group theory, discrete groups, and number theory : a conference in honor of Gerhard Rosenberger, December 8-9, 2004, Fairfield University, AMS Special Session on Infinite Groups, October 8-9, 2005, Bard College
This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.
eBook
Domains of discontinuity of Lorentzian affine group actions
We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of
R
n
.
Journal Article
Non-locally discrete actions on the circle with at most N fixed points
A subgroup of
Homeo
+
(
S
1
)
is Möbius-like if every element is conjugate to an element of
PSL
(
2
,
R
)
. In general, a Möbius-like subgroup of
Homeo
+
(
S
1
)
is not necessarily (semi-)conjugate to a subgroup of
PSL
(
2
,
R
)
, as discovered by Kovačević (Trans Am Math Soc 351:4823–4835, 1999). Here we determine simple dynamical criteria for the existence of such a (semi-)conjugacy. We show that Möbius-like subgroups of
Homeo
+
(
S
1
)
which are elementary (namely, preserving a Borel probability measure), are semi-conjugate to subgroups of
PSL
(
2
,
R
)
. On the other hand, we provide an example of elementary subgroup of
Diff
+
∞
(
S
1
)
satisfying that every non-trivial element fixes at most 2 points, which is not isomorphic to any subgroup of
PSL
(
2
,
R
)
. Finally, we show that non-elementary, non-locally discrete subgroups acting with at most
N
fixed points are conjugate to a dense subgroup of some finite central extension of
PSL
(
2
,
R
)
.
Journal Article
On the Geometry and Topology of Discrete Groups: An Overview
In this paper, we provide a brief introduction to the main notions of geometric group theory and of asymptotic topology of finitely generated groups. We will start by presenting the basis of discrete groups and of the topology at infinity, then we will state some of the main theorems in these fields. Our aim is to give a sample of how the presence of a group action may affect the geometry of the underlying space and how in many cases topological methods may help the determine solutions of algebraic problems which may appear unrelated.
Journal Article
Topological mixing of Weyl chamber flows
In this paper we study topological properties of the right action by translation of the Weyl chamber flow on the space of Weyl chambers. We obtain a necessary and sufficient condition for topological mixing.
Journal Article
Geometry, groups and dynamics : ICTS program : groups, geometry and dynamics, December 3-16, 2012, CEMS, Kumaun University, Almora, India
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.
eBook