|
I mostly work on symplectic topology and pseudoholomorphic curves. I like problems which are concrete or specialised but which serve to illustrate bigger principles. Here you can see a real cubic surface which I found on the Cubic Surfaces Homepage. |  |
|
Papers | Work in Progress | Summary | Problems | Talks | Thesis Papers...or you could just search for me on arXiv or me on MathSciNet.J. D. Evans and J. Kędra, Remarks on monotone Lagrangians in Cn, arXiv:1110.0927, submitted October 2011 J. D. Evans, Quantum cohomology of twistor spaces and their Lagrangian submanifolds, arXiv:1106.3959, submitted June 2011 J. D. Evans, The infimum of the Nijenhuis energy, arXiv:1109.4854, to appear in Mathematics Research Letters J. D. Evans, Symplectic mapping class groups of some Stein and rational surfaces, Journal of Symplectic Geometry 2011 9(1):45-82 or arXiv:0909.5622 J. D. Evans, Lagrangian spheres in Del Pezzo surfaces, Journal of Topology 2010 3(1):181-227 or arXiv:0902.0540 Work in ProgressI'm currently thinking a lot about monotone Lagrangian submanifolds, about families of symplectic manifolds (and their Gromov-Witten invariants) and about pseudoholomorphic curves in non-Kähler manifolds. I am also working on a page for the Manifold Atlas about pseudoholomorphic curves. Watch this space. SummaryMy research interests centre on topological problems in symplectic geometry. This has the exciting benefit of being connected to many other areas of mathematics including the geometry of complex projective varieties, the gauge theory of low-dimensional manifolds and the Riemannian geometry of 4-manifolds. In all these cases, the symplectic geometry of the spaces involved sees something very interesting. For a complex projective variety, you can use the symplectic mapping class group to detect holes in the moduli space of the variety. For a 3-manifold you can (conjecturally) recover its instanton Floer invariants from Lagrangian intersection theory in a moduli space of connections over a Heegaard surface (the Atiyah-Floer conjecture). For the twistor spaces of hyperbolic 4-manifolds, the pseudoholomorphic curves for a natural almost complex structure correspond via the twistor projection to branched minimal immersed surfaces in the 4-manifold (so Gromov-Witten invariants count something highly nontrivial from Riemannian geometry in this case). This diversity of contact with other beautiful areas of mathematics is one of the things that makes the study of symplectic manifolds worthwhile. ProblemsHere are some open problems which interest me and which I haven't yet been able to solve. I believe they may be very hard but that shouldn't stop one from trying. If you're interested/have an idea/want to collaborate on any of these or related problems, please get in touch!
TalksUpcoming
Past
ThesisI did my PhD from 2006-2010 at DPMMS, University of Cambridge under the supervision of Ivan Smith (here is my maths genealogy page to prove it!) and funded by a studentship from the Faulkes Foundation. My thesis is entitled "Symplectic topology of some Stein and rational surfaces", my examiners were Jarek Kędra and Gabriel Paternain, my viva was on 15th April 2010 and I graduated on 17th July 2010. You can read the thesis here and a page-long summary here. | |