## Departmental PhD Thesis Exam – Daniel Rowe

Everyone is welcome to attend.  Refreshments will be served in the Math Lounge before the exam.

Tuesday, June 16, 2015
3:10 p.m.
BA6183

PhD Candidate: Daniel Rowe
Supervisor:  Joel Kamnitzer
Thesis title:  Lusztig Slices in the Affine Grassmannian and Nilpotent Matrices

********************

Abstract:

The focus of this dissertation is to present some new results related to an isomorphism of Mirkovi\’c-Vybornov between Lusztig slices in the affine Grassmannian and varieties of nilpotent matrices. We give an explicit alternate Mirkovi\’c-Vybornov isomorphism in the $GL_{n}$-affine Grassmannian and an explicit isomorphism in the $GL_{2}$-affine Grassmannian. We also transport an additive action on the Lusztig slice through the Mirkovi\’c-Vybornov isomorphism and show that it corresponds to a residual conjugation action. We go on to verify that this additive action matches a previously discovered action on the Slodowy slice.

The thesis can be found here: thesis_rowe_jun 12 15