Algebraic Geometry Working Seminar

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"An Overview of the Gelfand-Cetlin System"

The Gelfand-Cetlin system is an integrable system first introduced by V. Guillemin and S. Sternberg in 1983 in order to study the quantization of complex flag varieties. This integrable system shares many properties with moment maps coming from torus actions, such as having a polytope as image and the fibres above the interior points of the polytope are Lagrangian tori. There is one big difference between toric moment maps and the Gelfand-Cetlin system: the latter allows for Lagrangian fibres which are not tori. This phenomenon makes this system an important object to study in the context of mirror symmetry.  In this talk, I will give a brief overview of the Gelfand-Cetlin system and discuss the classification by Y. Cho, Y. Kim and Y-G. Oh of the Lagrangian fibres.

MC 5417