15:30
Some geometry around torsion homology
Abstract
Given a space with some kind of geometry, one can ask how the geometry of the space relates to its homology. This talk will survey some comparisons of geometric notions of complexity with homological notions of complexity. We will then focus on hyperbolic 3-manifolds and the main result will replace a spectral gap problem related to torsion in homology with a geometric version involving geodesic length and stable commutator length. As an application, we provide "bad" examples of hyperbolic 3-manifolds with bounded geometry but extremely small (1-form) spectral gaps.
Join Optiver for end of academic year celebratory drinks and nibbles at The Alchemist on 12th June to chat with the team about life at Optiver and the opportunity to make an early application this summer. Feel free to bring a friend who could be interested in a role in trading, research or software engineering. 19:00-21:00, 12th June, The Alchemist, Westgate, Bonn Square, Oxford OX1 1TR