COmbinatorial and ALgebraic Aspects of Surface group representations.

SCHEME: AFR Bilateral Calls

CALL: 2017

DOMAIN: MT - Mathematics





HOST INSTITUTION: University of Luxembourg

KEYWORDS: Geometric structure, surface groups, character varieties, quasifuchsian manifolds, higher Teichmüller theory

START: 2019-03-01

END: 2021-02-28


Submitted Abstract

COALAS will extend and expand ongoing scientific relations between the Uni- versity of Luxembourg and the National University of Singapore in geometry. It is focused on character varieties and representations of surface groups in Lie groups. The project in- cludes 5 subprojects, each of which will require the joint expertise of the Luxembourg and Singapore groups. These projects rely on a variety of combinatorial, analytic, algebraic and geometric tools. WP1 is on pseudo-modular groups, recently discovered discrete subgroups of P SL(2, R) sharing some key properties with modular groups. WP2 is about identities on character varieties, and proposes a wide generalization of certain famous identities that have played an important role in recent developments in geometry. WP3 proposes a new viewpoint on classical quasifuchsian manifolds, centered on the role of their “measured lamination at infinity”. WP4 proposes to study representations of surface groups in certain Lie groups through the study of special surfaces. Finally, WP 5 is about specific aspects of spectral theory for higher Teichmüller theory, a topic which thanks to new techniques introduced by a member of the Singapore team, has only recently become tractable. The project will be conducted thanks to two 2-year postdoctoral fellows, to be hired in September 2018, located mainly in Luxembourg but who will spend 25% of their time at NUS. All necessary measures will be taken to attract top level candidates for these two positions, and to provide them with the best means in terms of career development. This will include participation in scientific events in their academic area (workshops, conferences, summer or winter schools, etc), close mentoring by established researchers all well versed in global academic strategy and access to an outstanding international network, and soft skills training.

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