Dr Paul Johnson
School of Mathematical and Physical Sciences
Lecturer in Pure Mathematics
+44 114 222 3775
Full contact details
School of Mathematical and Physical Sciences
J6b
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
- Profile
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I received my PhD from the University of Michigan in 2009. I was a postdoc at Imperial College, london from 2009-2011, and an NSF postdoc at Columbia University from 2011-2013. I was an assistant professor at the Colorado State University from 2013-2014 before joining Sheffield University in 2014.
- Research interests
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I study enumerative geometry, which aims to count geometric things, and leads to the interplay of geometry and combinatorics. Particular areas of focus are Gromov-Witten theory, which counts maps from curves into varieties, and Hilbert schemes of points on surfaces.
- Publications
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Featured publications
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All publications
Journal articles
- Counting curves on Hirzebruch surfaces : tropical geometry and the Fock space. Mathematical Proceedings of the Cambridge Philosophical Society, 171(1), 165-205.
- Lattice points and simultaneous core partitions. Electronic Journal of Combinatorics, 25(3). View this article in WRRO
- Double Hurwitz numbers via the infinite wedge. Transactions of the American Mathematical Society, 367(9), 6415-6440. View this article in WRRO
- Equivariant GW Theory of Stacky Curves. Communications in Mathematical Physics, 327(2), 333-386. View this article in WRRO
- THE QUANTUM LEFSCHETZ HYPERPLANE PRINCIPLE CAN FAIL FOR POSITIVE ORBIFOLD HYPERSURFACES. MATHEMATICAL RESEARCH LETTERS, 19(5), 997-1005.
- The quantum Lefschetz hyperplane principle can fail for positive orbifold hypersurfaces. Mathematical Research Letters, 19(5), 997-1005. View this article in WRRO
- Wall crossings for double Hurwitz numbers. Advances in Mathematics, 228(4), 1894-1937. View this article in WRRO
- Abelian Hurwitz-Hodge integrals. The Michigan Mathematical Journal, 60(1), 171-198. View this article in WRRO
- Tropical Hurwitz numbers. Journal of Algebraic Combinatorics, 32(2), 241-265. View this article in WRRO
Chapters
- Hurwitz numbers, ribbon graphs, and tropicalization In Athorne C, Maclagan D & Strachan I (Ed.), Tropical geometry and integrable systems (pp. 55-72). American Mathematical Society View this article in WRRO
Conference proceedings papers
- Counting curves on Hirzebruch surfaces : tropical geometry and the Fock space. Mathematical Proceedings of the Cambridge Philosophical Society, 171(1), 165-205.
- Research group
- Teaching activities
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MAS332 Complex Analysis MAS341 Graph Theory MAS439 Commutative Algebra and Algebraic Geometry