Back to Departmental Colloquium: Fall 2021
Departmental Colloquium
Date: Thursday, Oct 21, 2021
Time: 4:00PM
Location: JWB 335
Alan Reid
Rice University
Title |
The geometry, topology and arithmetic of Bianchi orbifolds and their finite covers |
Abstract |
Let d be a square-free positive integer, and let O d denote the ring of integers in Q (sqrt(− d) ). Then the groups PSL (2, O d ) are known as the Bianchi groups, and are a natural generalization of the modular group PSL (2, Z ). The Bianchi groups are discrete subgroups of PSL (2, C ), and as such act discontinuously on H 3. The quotient Bianchi orbifolds, Q d = H 3 / PSL (2, O d ) are non-compact finite volume hyperbolic 3-orbifolds with h d (class number of O d ) cusps. These represent the totality of commensurability classes of non-compact arithmetic hyperbolic 3 -orbifolds. This talk will survey some recent and not so recent work on understanding the geometry and topology of these orbifolds, their covers and connections to number theory. |
Number Theory
Commutative Algebra
Topology