May 4: Mboyo Esole (Harvard)

Title:  Incidence geometry and resolutions of Weierstrass models 
 
Time: 2pm
Place: 4N9
 
Abstract: In this talk, I  will present several new results in the geometry of elliptic fibrations: 
In the first part of the talk, I  will introduce an incidence geometry described by a representation of a given Lie algebra and explain how it contains a natural poset structure reminiscent of a Gelfand-Tsetlin pattern. This poset provides  a simple counting of flats and ensembles of the incidence geometry. For an elliptic fibration, it is understood as a counting of (partial) crepant resolutions.  In a physical context, the counting is interpreted as a detailed  enumeration of mixed Coulomb-Higgs branches of a five dimensional gauge theory with 8 supercharges.   In particular, I will present a  generating function counting the  mixed Coulomb-Higgs phases of a U(n) gauge theories with matter in the fundamental and anti-fundamental representations. 
In the second part of the talk, I will describe the network of crepant resolutions of a SU(2) SU(3)  gauge theory modeled by an elliptic fibration. This provides a fully resolved description of models studied recently by Grassi-Halverson-Shanesonn-Taylor. I will explain how representation theory aspects are retrieved by a simple analysis of intersection numbers.