Title:Systoles and Coxeter groups
Speaker:Olivier Mathieu(CNRS,Lyon)
Time:Monday, May6, 2024, 15:30-16:30
Venue:Mingde Building B201-1
Abstract:Given a closed hyperbolic surface, asystoleis a closed geodesic of shortestlength. A generic surface of genus
has a unique systole which cuts itinto one or two noncontractible pieces. However, there are closed hyperbolicsurfaces of genus
, whose set of systolesfillsthe surface, i.e. it cuts thesurface into polygons. In general, it is easy to find surfaces with a largenumber of systoles which fill. A classical example is the Bolsa surface ofgenus 2 with 12 systoles.Here we are interested to find surfaces for which the set of systoles is fillingwhile being small. In fact, our approach provides surfaces with significativelyless systoles than the previously known examples. Then we will briefly outlinea consequence in Teichmüllertheory.Our construction is based on the theory of Coxeter groups, especially thearithmetic properties of the Tits representation. From a geometric viewpoint,it involves hyperbolictessellations. Although this work mixes hyperbolic geometryand representation theory, our presentation will be quite elementary.
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Olivier Mathieu Domain: Representation Theory Senior CNRS Researcher Invited speaker at the ICM (Kyoto 1990) Grant Sloan fellowship (1991-94) Grand Prix IBM-France (1992) Plenary Speaker of the first joint Brazil-France Conference, 2019 (Rio) Jose Adem Memorial Lectures Series, 2019 (Mexico) |
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