Seminars
This week's seminars
Pure Maths Colloquium: Quasispheres and Expanding Thurston maps
11 February 2019 16:00 in CM219
A quasisymmetric map is one that changes angles in a controlled way. As such they are generalizations of conformal maps and appear naturally in many areas, including Complex Analysis and Geometric group theory. A quasisphere is a metric sphere that is quasisymmetrically equivalent to the standard $2$-sphere. An important open question is to give a characterization of quasispheres. This is closely related to Cannon's conjecture. This conjecture may be formulated as stipulating that a group that ``behaves topologically'' as a Kleinian group ``is geometrically'' such a group. Equivalently, it stipulates that the ``boundary at infinity'' of such groups is a quasisphere.
A Thurston map is a map that behaves ``topologically'' as a rational map, i.e., a branched covering of the $2$-sphere that is postcritically finite. A question that is analog to Cannon's conjecture is whether a Thurston map ``is'' a rational map. This is answered by Thurston's classification of rational maps.
For Thurston maps that are expanding in a suitable sense, we may define ``visual metrics''. The map then is (topologically conjugate) to a rational map if and only if the sphere equipped with such a metric is a quasisphere. This talk is based on joint
work with Mario Bonk.
Contact anna.felikson@durham.ac.uk for more information
Research Seminars by Series
The research groups in the Department of Mathematical Sciences hold several seminar series in term time. Information on date, time and location are available here.
For information on previous years' seminars please see the seminar archives pages.