PhD studentship in Geometry at Universitat Autònoma de Barcelona

The topic of the thesis should fit the objectives of the research project: Geometry of Symmetric Spaces (MTM2012-34834), funded by the Ministerio de Economía y Competitividad, Spain (see a description below).

Principal investigator: Joan Porti, Universitat Autònoma de Barcelona
Contact e-mail: porti@mat.uab.cat

How to apply and further information on
http://www.idi.mineco.gob.es/portal/site/MICINN/menuitem.dbc68b34d11ccbd5d52ffeb801432ea0/?vgnextoid=68eb71d255dcf310VgnVCM1000001d04140aRCRD

Deadline for applications: September 10, 2013, 15:00 (Barcelona time).
Tentative starting date: January 2014.
Applicants must hold a Bachelor degree in Mathematics and preferably also a Master’s degree in Mathematics.
Salary: work contract of 16,422 € each year (gross) for four years. Full time dedication.

Project Summary

We will study different aspects of the geometry of symmetric spaces: geometric structures, actions of thin groups and integral geometry. More precisely the questions are:

  1. We rise the study of the space of representations of groups in the isometries of a symmetric spaces, either locally (deformations) and globally (moduli spaces). We want to study geometric structures associated to those representations, with special interest in projective structures.
  2. We aim to understand the action of thin groups in the ideal boundary of a symmetric space of higher rank. The goal is to describe the dynamics in terms of the Tits building structure, in particular we seek for discontinuity domains at infinity, if possible cocompact.
  3. We want to develop integral geometry in symmetric spaces, starting with rank one, taking the approach of valuations. We aim to deepen the results for complex projective and hyperbolic spaces and to extend them to quaternionic spaces (projective, hyperbolic and affine).
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