Contact
I am a Reader in Mathematics in the Algebra & Geometry section of the Department of Mathematics and Statistics at the University of Lancaster.
- Email:
- j.d.evans@lancaster.ac.uk
- Address:
- Department
of Mathematics and Statistics,
University of Lancaster,
Bailrigg LA1 4YW - Office:
- B64, B Floor, Fylde College
- Web:
- http://jde27.uk
Research
I work on problems in geometry and topology. I am particularly interested in the symplectic topology of algebraic varieties.
Joint with Yanki Lekili and Ailsa Keating, I run the Free Mathematics Seminar (currently on hiatus).
Support
- 2022-26
- EPSRC Grant EP/W015749/1 "New Frontiers in Symplectic Topology" (joint with YankI 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
- Past PhD students
- Emily Maw, Momchil Konstantinov, Tobias Sodoge
- Past postdocs
- Angelica Simonetti, Daniel Cavey, Jack Smith.
Collaborators
- Nikolas Adaloglou
- Georgios Dimitroglou Rizell
- Ailsa Keating
- Jarek Kędra
- Yankı Lekili
- Mirko Mauri
- Angelica Simonetti
- Ivan Smith
- Renato Vianna
- Giancarlo Urzúa
Papers/books/preprints
- Lagrangian Klein bottles in S2 x S2
- with Nikolas Adaloglou, arxiv:2410.07782
- Lagrangian surplusection phenomena
- with Georgios Dimitroglou Rizell, arXiv:2408.14883
- 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
- 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
Talk notes/videos
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)
Useful links
Lancaster students or staff may find the following links useful:
- Module and Programme Catalogue
- Part II Handbook (out of date, but still some useful info)
- The ASK service (all-purpose student enquiry desk at Lancaster: very knowledgeable and helpful)
- Disability services
- Counselling and mental health services
- Change of module
- Change of programme
- Exceptional Circumstances page (for if your coursework or exam results have been adversely affected by circumstances beyond your control).
- Intercalation (if you want to interrupt your studies for a year)