Adam Gal

I am currently a PDRA in Oxford University and a stipendiary lecturer in St. Peter's College.

Research Interests:
Categorification, Hall algebras, Representation theory, Higher categories. 
My current focus is on categorifying Hall algebras via a geometric approach building on the work of Dyckerhoff and Kapranov. I am interested in studying the underlying geometric structure that controls the different kinds of Hall algebras and using fundamental observations about it to deduce concrete results in the specific cases.
In earlier work we introduced a notion of higher Hopf algebra, of which the geometric Hall algebra construction is an example. 

Symmetric self-adjoint Hopf categories and a categorical Heisenberg double (joint with Elena Gal), 2014, to appear in Q.J.Math

Autoequivalences of the category of schemes (joint with Avraham Aizenbud)

A geometric approach to Hall algebras II: The bialgebra structure (joint with Elena Gal and Kobi Kremnizer), in preparation

Recovering the braiding on Rep(GLn, Fq) via an extension of the Waldhausen construction (joint with Elena Gal and Mark Penney), in preparation

Contact info:
Andrew Wiles building,
ROQ, Woodstock road, 
OX2 6GG, Oxford, UK