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.
D. Gabai, R. Meyerhoff, N. Thurston, and A. Yarmola, Enumerating
Kleinian groups
W. A. de Graaf, Exploring Lie theory with GAP
A. S. Detinko, D. L. Flannery, and A. Hulpke, Freeness and $S$-arithmeticity
of rational Mobius groups
J. Gilman, Computability models: Algebraic, topological and geometric
algorithms
W. M. Goldman, Compact components of planar surface group representations
A. Hulpke, Proving infinite index for a subgroup of matrices
M. Kapovich, Geometric algorithms for discreteness and faithfulness
M. Kapovich, A. Detinko, and A. Kontorovich, List of problems on discrete
subgroups of Lie groups and their computational aspects
A. Mark, J. Paupert, and D. Polletta, Picard modular groups generated by
complex reflections
J. M. Riestenberg, Verifying the straight-and-spaced condition
T. N. Venkataramana, Unipotent generators for arithmetic groups
Alla Detinko, University of Huddersfield, United Kingdom.
Michael Kapovich, University of California, Davis, CA.
Alex Kontorovich, Rutgers University, New Brunswick, NJ.
Peter Sarnak, Institute for Advanced Study, Princeton, NJ.
Richard Schwartz, Brown University, Providence, RI.
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