Students

I am available for the supervision a master thesis. I can suggest the following research topics, but I am also eager to hear your suggestions.

Vertex operators and symmetric functions

This project aims to study Jing's construction of Hall-Littlewood polynomials using vertex operators (see his paper here), and explore the connection with free field representations of shifted quantum groups. 

Shifted quantum groups

This project explores the relation between quantum toroidal algebras and shifted quantum affine algebras in certain crystal limits. This study has important implications for the non-perturbative description of gauge theories using brane systems. It is based on my recent work that can be found here.

Algebraic approach to topological strings

This research project is based on the 'algebraic engineering' techniques, a new framework that extends the technique of topological strings theory using the representation theory of quantum groups. The main goal is to derive the integrable properties of certain strings amplitudes. A good review on topological strings can be found here.