Paul Johnson

Dr. Paul Johnson is a Lecturer in Pure Mathematics at the School of Mathematical and Physical Sciences, University of Sheffield. He holds a PhD from the University of Michigan (2009) and has held postdoctoral positions at Imperial College London (2009-2011) and Columbia University as an NSF postdoc (2011-2013). Prior to joining Sheffield in 2014, he was an Assistant Professor at Colorado State University (2013-2014).

His research focuses on enumerative geometry, exploring the interplay between geometry and combinatorics. Key areas include Gromov-Witten theory, which counts maps from curves to algebraic varieties, and Hilbert schemes of points on surfaces. He is affiliated with the Pure Mathematics cluster and Topology research groups within the school.

Dr. Johnson teaches advanced undergraduate and graduate courses such as MAS332 Complex Analysis, MAS341 Graph Theory, and MAS439 Commutative Algebra and Algebraic Geometry. His publications span topics in algebraic geometry, tropical geometry, and combinatorics, with notable contributions to Hurwitz numbers, moduli spaces, and Fock space applications.

His work demonstrates a strong emphasis on geometric structures and their combinatorial interpretations, with applications to mathematical physics and topology. He maintains an active research group and contributes to the academic community through teaching and mentorship.