About me

Minh Lam Nguyen

Department of Mathematics, Michigan State University

Email: nguy1941@msu.edu,  minhn@wustl.edu

ORCID, Google Scholar

Hello! I am currently a Postdoc Research  Associate at Michigan State University, working with Matt Stoffregen. Previously, I was 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-theoretic Floer homology theories. 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 for Ph.D., I'm interested in other variants of generalization to Seiberg-Witten equations and exploring their applications in low-dimensional topology and special holonomy geometry. Currently, I'm working on filtered versions of various Floer homology theories (instanton and monopole) inspired by persistence homology techniques from topological data analysis with an eye to applications to geometry and topology.

I completed my PhD in May 2022.