# Jonny Evans's Homepage

Research (Group | Papers | Talks)

- Jonny Evans, j.d.evans • ucl.ac.uk
- Room 802a, Department of Mathematics,
- UCL, Gower Street, London, WC1E 6BT

#### Quick links

- — UCL Geometry and Topology Group and Seminar.
- — Symplectic Cut Seminar.
- — London School of Geometry and Number Theory.
- — My new blog, my old blog and Youtube channel.
- — Mathematical Field Notes: Mostly written to remind me of stuff I've told my PhD students.
- — A visual guide to the UCL undergraduate mathematics course (and source code)
- — CV.

## Teaching

### Current

- — MATH0074: Topology and Groups
- — Fourth-year projects
- — Mathematical reading, good books and thoughts on undergraduate research

### Previous

- — Geometry and Groups (UCL 2015, 2016).
- — Lie Groups and Lie Algebras (UCL 2013, 2014, 2015, 2016).
- — Mathematical Methods 3 (UCL 2012, 2013, 2014).
- — Aspects of Yang-Mills theory (24 lecture graduate course, ETH 2011).
- — First course in symplectic topology (21 lecture graduate course, ETH 2010).
- — 2013-2014 E-learning project: Video lectures filmed by students.

## Research

I am particularly interested in the interface between symplectic topology and algebraic geometry. I am supported by EPSRC Grant EP/P02095X/1.

### Group

#### Current members

- — Momchil Konstantinov (LSGNT PhD student, started 2014)
- — Emily Maw (LSGNT PhD student, started 2015)
- — Jack Smith (EPSRC postdoctoral researcher, started 2017)
- — Angela Wu (LSGNT PhD student, jointly supervised with Steven Sivek, started 2017)

#### Past members

- — Tobias Sodoge (started 2013, graduated 2017)

#### Collaborators

### Papers

Me on arXiv and MathSciNet.

**Antiflips, mutations, and unbounded symplectic embeddings of rational homology balls.**- with G. Urzúa
- arXiv:1807.06073 preprint 2018.

**Bounds on Wahl singularities from symplectic topology.**- with I. Smith
- arXiv:1708.02268 preprint 2017.

**Markov numbers and Lagrangian cell complexes in the complex projective plane.**- with I. Smith
- arXiv:1606.08656 or Geometry & Topology (2018) 22(2):1143-1180.

**Generating the Fukaya categories of Hamiltonian G-manifolds.**- with Y. Lekili
- arXiv:1507.05842 to appear in Journal of the American Mathematical Society.

**Exotic spheres and the topology of symplectomorphism groups.**- with G. Dimitroglou Rizell
- arXiv:1407.3173 or Journal of Topology (2015) 8(2):586-602.

**Floer cohomology of the Chiang Lagrangian.**- with Y. Lekili
- arXiv:1401.4073 or Selecta Mathematica (2015) 21(4):1361-1404.

**Unlinking and unknottedness of Lagrangian submanifolds.**- with G. Dimitroglou Rizell
- arXiv:1211.6633 or Geometry & Topology, (2014) 18:997-1034.

**Pseudoholomorphic tori in the Kodaira-Thurston manifold.**- with J. Kędra
- arXiv:1205.1239 or Compositio Mathematica (2015) 151(12) 2212-2250.

**Remarks on monotone Lagrangians in C**^{n}.- with J. Kędra
- arXiv:1110.0927 or Mathematical Research Letters (2014) 6:1241-1255.

**The infimum of the Nijenhuis energy.**- arXiv:1109.4854 or Mathematical Research Letters, (2012) 19(2):383-388.

**Quantum cohomology of twistor spaces and their Lagrangian submanifolds.**- arXiv:1106.3959 or Journal of Differential Geometry, (2014) 96(3)353-397.

**Symplectic mapping class groups of some Stein and rational surfaces.**- arXiv:0909.5622 or Journal of Symplectic Geometry (2011) 9(1):45-82.

**Lagrangian spheres in Del Pezzo surfaces.**- arXiv:0902.0540 or Journal of Topology (2010) 3(1):181-227.

### Selected talks (notes/videos)

- —
*Lagrangian cell complexes and Markov numbers*- Institute for Advanced Study (September 2016): video.

- —
*Exotic spheres and the topology of symplectomorphism groups* - —
*Lectures on symplectic and algebraic geometry*- UK-Japan Mathematical Forum (January 2013): one, two, three and accompanying blog post.

- —
*The quantum cohomology of twistor spaces*- CAST Workshop, Madrid (February 2012), slides.

- —
*Lagrangian spheres in Del Pezzo surfaces* - —
*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 (UCL and ETH).

## Elsewhere on the internet

- — The Cost of Knowledge.
- — The Faulkes Foundation who funded my PhD and who also fund excellent projects such as the Faulkes Telescope Project, which allows schoolchildren to remotely operate powerful telescopes in Hawaii.
- — All the talk notes and teaching materials available from this site are released under a CC-BY-SA 3.0 Licence. That means you're free to use them as long as you give appropriate attribution and release derivatives under an isomorphic licence.
- — My wife (occasionally) blogs about libraries.