Integrable Hierarchies, Solitons and Infinite Dimensional Algebras
Non-associative algebraic structures and integrable evolution systems
Grant number: | 12/04707-9 |
Support Opportunities: | Scholarships in Brazil - Doctorate |
Start date: | June 01, 2012 |
End date: | February 29, 2016 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
Principal Investigator: | Igor Mencattini |
Grantee: | Eber Daniel Chuno Vizarreta |
Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Associated scholarship(s): | 14/08512-3 - Cluster algebras and integrable systems, BE.EP.DR |
Abstract The theory introduced by Fock-Goncharov, called Higher Teichmüller Theory (HTT), is a huge generalization of the classical Teichmüller theory. It has as main ingredients a compact oriented surface S and a semisimple algebraic group G. The HTT provides a description of the space of the so called positive representations of the fundamental group of the surface S into G, showing that these are faithful, discrete and hyperbolic. The goal of this project is to apply the HTT to give a cluster algebras interpretation of a class of integrable systems which are naturally defined on the moduli spaces of $SL_{n}$-local systems on the genus 1 surfaces with a puncture. We also seek understanding the relevance of the HTT in the study of representations of the fundamental group of the surface S into PU(2,1) (the group of holomorphic isometries of the complex hyperbolic space). Such representation are related to the construction of complex hyperbolic geometry. | |
News published in Agência FAPESP Newsletter about the scholarship: | |
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