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# Geometry and Topology Seminar

## Warwick Mathematics Institute, Term I, 2018-2019

 Thursday October 4, 15:00, room MS.03 Maxime Fortier Bourque (Glasgow) Local maxima of the systole function Abstract: The systole of a hyperbolic surface is the length of its shortest closed geodesic(s). Schmutz Schaller initiated the study of the systole function and its local maxima in the 90's. I will explain a construction of a new infinite family of closed hyperbolic surfaces which are local maxima for the systole. The simplest of these surfaces is the Bolza surface, which is the surface of genus two with the largest number of symmetries. In higher genus, we obtain super-exponentially many examples and most of them have a trivial automorphism group. This is joint work with Kasra Rafi.

 Thursday October 11, 15:00, room MS.03 None (None) None Abstract: None

 Thursday October 18, 15:00, room MS.03 None (None) None Abstract: None

 Thursday October 25, 15:00, room MS.03 None (None) None Abstract: None

 Thursday November 1, 15:00, room MS.03 Peter Smillie (IHES, Caltech) Hyperbolic surfaces in Minkowski three-space Abstract: I’ll present a characterization of all hyperbolic surfaces properly isometrically embedded in Minkowski three-space. I'll then apply this characterization in the case where the hyperbolic surface is invariant under a discrete subgroup of isometrics of Minkowski space, and explore how this might help to understand these discrete subgroups. This is joint work with Francesco Bonsante and Andrea Seppi.

 Thursday November 8, 15:00, room MS.03 Stergios Antonakoudis (Cambridge) On totally geodesic subvarieties of moduli spaces Abstract: We will show that holomorphic isometries between Teichmüller spaces of closed Riemann surfaces in their Teichmüller metrics are geometric. That is, they are obtained from covering constructions of the underlying surfaces. We will also discuss recent progress on the study of real and complex totally geodesic submanifolds of Teichmüller and moduli spaces in dimensions two or more.

 Thursday November 15, 15:00, room MS.03 David Hume (Oxford) The geometric subgroup problem Abstract: One central aspect of Geometric Group Theory is the study of finitely generated groups; specifically relating their algebraic and geometricproperties. Geometrically, we consider groups up to quasi-isometry and we possess a wealth of tools to distinguish different quasi-isometry classes of groups. Algebraically, groups are studied via their subgroup structure. However, there are very few geometric properties of groups which pass to all their (finitely generated) subgroups, which is unsurprising given the number of classes of geometrically nice groups with wild subgroup behaviour. In this talk I will introduce a new spectrum of geometric invariants which behave monotonically with respect to subgroups (in the same way that the growth function does), and demonstrate that they do give new insight, particularly in the case of subgroups of hyperbolic groups.

 Thursday November 22, 15:00, room MS.03 None (None) TBA Abstract: None

 Thursday November 29, 15:00, room MS.03 Sebastian Hensel (Munich) (Un)distorted stabilisers in the handlebody group Abstract:In the mapping class group of a surface, stabilisers of curves are quasi-isometrically embedded for all curves. In this talk, we study a similar question for mapping class groups of 3-dimensional handlebodies and find a different picture (analogous to the situation in $\Out(F_n)$): stabilisers of meridians are quasi-isometrically embedded, while stabilisers of other curves may be exponentially distorted.

 Thursday December 6, 15:00, room MS.03 None (None) None Abstract: None

Information on past talks. This line was last edited Sat 3 Feb 2018 16:45:46 GMT