I am a lecturer in pure maths at the University of Glasgow. My office number is 527 in the department of mathematics and statistics. My research is in Donaldson-Thomas theory and cohomological Hall algebras, with a focus on applications to cluster algebras, nonabelian Hodge theory and geometric representation theory. At the moment I am particularly interested in the mathematical formulation of BPS Lie algebras, and using cohomological DT theory to understand nonabelian Hodge theory and the interface between string theory and geometric representation theory. All of this comes under the umbrella of utilising the cohomological integrality theorem in noncommutative DT theory, a joint work with Sven Meinhardt. Here is a talk I gave at the Fields Institute in 2016 on how that works. And here is a talk I gave at the Perimeter institute in 2017 on the definition of the BPS Lie algebra associated to a genus g surface. You can get hold of me at bdjdavison at gmail dot com. . |