Contact

I am a Reader in Mathematics in the Algebra & Geometry group of the School of Mathematical Sciences at Lancaster University.

Email:
j.d.evans@lancaster.ac.uk
Address:
School of Mathematical Sciences,
Lancaster University,
Bailrigg LA1 4YW
Office:
B64, B Floor, Fylde College
Web:
http://jde27.uk
Fells
Fells

Research

I work on problems in geometry and topology. I am particularly interested in the symplectic topology of algebraic varieties.

Together with Paul Biran and Gabriel Paternain, I am one of the editors for a special issue of the diamond open-access journal SIGMA (Symmetry, Integrability, Geometry: Methods and Applications). The special issue will focus on geometry and dynamics and will be produced in memory of Will Merry. See here for more information. If you are interested in contributing, don't hesitate to get in touch; the deadline for submissions is 31st January 2026.

Support

2022-26
EPSRC Grant EP/W015749/1 "New Frontiers in Symplectic Topology" (joint with Yankı Lekili).
2017-20
EPSRC Grant EP/P02095X/2 "Singularities and Symplectic Topology" (formerly known as EP/P02095X/1)

Research group

Current PhD students
Patrick Ramsey, Matt Buck, Elliot Gathercole
Current postdocs
Kai Hugtenburg
Mykola Matviichuk
Matt Habermann (EPSRC Postdoctoral Fellow)
Past PhD students
Emily Maw, Momchil Konstantinov, Tobias Sodoge
Past postdocs
Angelica Simonetti, Daniel Cavey, Jack Smith.

Collaborators

From 2020-21, I co-organised the Free Mathematics Seminar jointly with Yankı and Ailsa; many of the videos are still available and well worth watching.

Papers/books/preprints

Lagrangian Klein bottles in S2 x S2
with Nikolas Adaloglou, arxiv:2410.07782
To appear in Commentarii Mathematici Helvetici.
Lagrangian surplusection phenomena
with Georgios Dimitroglou Rizell, arXiv:2408.14883
SIGMA 20 (2024) 109.
Tropical methods for stable Horikawa surfaces
with Angelica Simonetti and Giancarlo Urzúa, arXiv:2405.02735
KIAS Lectures on Symplectic Aspects of Degenerations
arXiv:2403.03519
Noncommutative crepant resolutions of cAn singularities via Fukaya categories
with Y. Lekili, arXiv:2307.06592
Lectures on Lagrangian torus fibrations.
a book, arXiv:2110.08643
London Mathematical Society Student Texts Series, Number 105 (Cambridge University Press), 2023.
Symplectic cohomology of compound Du Val singularities.
with Y. Lekili, arXiv:2104.11713
Annales Henri Lebesgue, Volume 6 (2023), pp. 727-765.
A Lagrangian Klein bottle you can't squeeze.
arXiv:2009.01546
Journal of Fixed Point Theory and Applications Volume 24 (2022) Article number 47,
in Symplectic geometry - A Festschrift in honour of Claude Viterbo’s 60th birthday
Constructing local models for Lagrangian torus fibrations.
with M. Mauri, arXiv:1905.09229
Annales Henri Lebesgue, Volume 4 (2021), pp. 537-570.
Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls.
with G. Urzúa, arXiv:1807.06073
Annales de l'Institut Fourier, Volume 71 (2021) no.5 pp. 1807-1843.
Bounds on Wahl singularities from symplectic topology.
with I. Smith, arXiv:1708.02268
Algebraic Geometry, (2020) 1(1) 59-85.
Markov numbers and Lagrangian cell complexes in the complex projective plane.
with I. Smith, arXiv:1606.08656
Geometry & Topology (2018) 22(2):1143-1180.
Generating the Fukaya categories of Hamiltonian G-manifolds.
with Y. Lekili, arXiv:1507.05842
Journal of the American Mathematical Society (2019) 32:119-162.
Exotic spheres and the topology of symplectomorphism groups.
with G. Dimitroglou Rizell, arXiv:1407.3173
Journal of Topology (2015) 8(2):586-602.
Floer cohomology of the Chiang Lagrangian.
with Y. Lekili, arXiv:1401.4073
Selecta Mathematica (2015) 21(4):1361-1404.
Unlinking and unknottedness of Lagrangian submanifolds.
with G. Dimitroglou Rizell, arXiv:1211.6633
Geometry & Topology, (2014) 18:997-1034.
Pseudoholomorphic tori in the Kodaira-Thurston manifold.
with J. Kędra, arXiv:1205.1239
Compositio Mathematica (2015) 151(12) 2212-2250.
Remarks on monotone Lagrangians in Cn.
with J. Kędra, arXiv:1110.0927
Mathematical Research Letters (2014) 6:1241-1255.
The infimum of the Nijenhuis energy.
arXiv:1109.4854
Mathematical Research Letters, (2012) 19(2):383-388.
Quantum cohomology of twistor spaces and their Lagrangian submanifolds.
arXiv:1106.3959
Journal of Differential Geometry, (2014) 96(3)353-397.
Symplectic mapping class groups of some Stein and rational surfaces.
arXiv:0909.5622
Journal of Symplectic Geometry (2011) 9(1):45-82.
Lagrangian spheres in Del Pezzo surfaces.
arXiv:0902.0540
Journal of Topology (2010) 3(1):181-227.

Translations

On Amicable Numbers (an English translation of Euler's De Numeris Amicabilibus E152)
arXiv:2409.08783

Talk notes/videos

Symplectic cohomology of compound Du Val singularities
Lisbon Geometry Seminar (Feb 2022)
A Lagrangian Klein bottle you can't squeeze
Western Hemisphere Virtual Symplectic Seminar (Sep 2020)
Symplectic embeddings of rational homology balls
Glasgow Topology Seminar (October 2019): YouTube version
KIAS Lectures on Symplectic aspects of degenerations
Three lectures given at the 2019 ASADCS conference in Seoul: notes
Lagrangian cell complexes and Markov numbers
Institute for Advanced Study (September 2016): video
Exotic spheres and the topology of symplectomorphism groups
Simons Center for Geometry and Physics (August 2014): video and slides
Lectures on symplectic and algebraic geometry
UK-Japan Mathematical Forum (January 2013): notes from Lecture 1, Lecture 2, Lecture 3 and accompanying blog post
The quantum cohomology of twistor spaces
CAST Workshop, Madrid (February 2012), slides
Lagrangian spheres in Del Pezzo surfaces
Lyon, February 2011 and Oxford, April 2010
Symplectic Picard-Lefschetz theory (expository, mostly pictures!)
Slides from a colloquium I gave in Neuchâtel (April 2012).
Luttinger surgery (expository)
ENS Lyon (January 2012) expository notes
Slides/notes from successful job/postdoc talks
Lancaster, UCL, ETH
Image of developing map for an almost toric structure on CP2
Image of developing map for an almost toric structure on CP2.

Teaching

Current
Numerical and Analytical Methods in Engineering (Lancaster 2024-)
Algebraic curves (Lancaster 2022-)
Past
Lie Groups and Lie Algebras (Lancaster 2020-2023, UCL 2013-2016)
Linear Algebra (Lancaster 2019-2022)
Lagrangian torus fibrations (LTCC 2019)
Topology and Groups (UCL 2018-2019)
Geometry and Groups (UCL 2015-2016)
Mathematical Methods 3 (UCL 2012-2014)
Aspects of Yang-Mills Theory (ETH 2011)
First course in symplectic topology (ETH 2010)

Other