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Dr Jonny Evans
Room 501
Department of Mathematics, UCL
Gower Street
London
WC1E 6BT
Appointment
  • Lecturer
  • Dept of Mathematics
  • Faculty of Maths & Physical Sciences
 
 
Research Groups
Research Summary
I'm particularly interested in global problems in geometry, specifically in symplectic geometry where many global problems live on a knife edge between "soft" (amenable to solution by an h-principle) and "hard" (displaying rigidity and requiring deep geometric techniques to tackle them). I like to study examples and concrete problems. My work to date falls into three main categories:

Lagrangian submanifolds in symplectic manifolds: Understanding their smooth and Hamiltonian knotting; understanding their 'quantum' invariants (i.e. holomorphic disc counts); in a given ambient space (like Del Pezzo surfaces or Cn), classifying them or finding restrictions on their topology.

Holomorphic curves in symplectic manifolds: Calculating quantum cohomology rings and computing (family) Gromov-Witten invariants for specific non-Kaehler examples (twistor spaces and nilmanifolds); more generally, holomorphic curves arise as a tool in everything I do.

Symplectomorphism groups: Computing their homotopy groups; trying to understand their classifying spaces in terms of spaces of almost complex structures and in terms of moduli spaces of projective varieties.
Academic Background
2010 PhD Doctor of Philosophy University of Cambridge
2006 MMath Master of Mathematics University of Cambridge
2005 BA Bachelor of Arts University of Cambridge
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