Minh Lam Nguyen
Department of Mathematics and Statistics, Washington University in St Louis
Hello! I am currently a Postdoc at Washington University in St Louis, working with Ali Daemi. I finished my PhD at the University of Arkansas. My advisors were Jeremy Van Horn-Morris and John Ryan. My research interest is in low-dimensional topology and gauge theory. Specifically during my PhD, I was interested in the applications of the Rarita-Schwinger operator to gauge theory in 4-dimensional topology.
The basic idea of gauge theory is to associate a smooth manifold with a moduli space and to prove that invariants of the moduli space are also invariants of the smooth manifold. The gauge-theoretic moduli spaces often come from solution spaces of certain partial differential equations in particle physics which are defined in terms of geometric objects such as connections and spinors, modulo some group of gauge symmetries.
The majority of my research and PhD dissertation focuses on the technique of finite-dimensional approximation and computations in Pin(2)-equivariant K-Theory but applies to the setting where the Rarita-Schwinger operator replaces the usual Dirac operator in the Seiberg-Witten equations. Right now, besides following up on my work during Ph.D., I'm interested in other variants of generalization to Seiberg-Witten equations and exploring their applications in low-dimensional topology and complex/Kahler geometry. I'm also expanding my research toolkit in areas of geometric topology, knot theory, etc.
I completed my PhD in May 2022.