Alexander F. Ritter Professor of Mathematics University of Oxford CV 2009 PhD (M.I.T.) 2005 MSc (UChicago) 2004 MMath (Cambridge, Trinity Coll.) 2003 BA (Cambridge, Trinity Coll.)

Research Interests Symplectic topology Mirror symmetry Floer homology Fukaya categories String topology.

⋄ Recent slides from a talk in 2025: Equivariant Floer theory for symplectic C*-manifolds.

⋄ Recent course taught in 2024: Morse Homology (TCC Graduate course) : Lecture notes here.

For potential PhD students: interested in doing a Ph.D. in geometry at Oxford under my guidance? here's a brief survey of symplectic topology, Floer theory and Fukaya categories, and a summary of some of my work (and here's an older survey in 10 slides!) (If you do apply, keep in mind that early applications, say in November, are more likely to obtain scholarship funding)

Research articles ♦ Quantum cohomology and Floer invariants of semiprojective toric manifolds (joint with F. Živanović) (2025, arXiv:2501.09011) ♦ Filtrations on equivariant quantum cohomology and Hilbert-Poincaré series (joint with F. Živanović) (2024, arXiv:2410.17237) ♦ Filtrations on quantum cohomology via Morse-Bott-Floer Spectral Sequences (joint with F. Živanović) (2023, arXiv:2304.14384) ♦ Filtrations on quantum cohomology from the Floer theory of C*-actions (joint with F. Živanović) (2023, arXiv:2304.13026) ♦ The McKay correspondence for isolated singularities via Floer theory (joint with M. McLean) (Journal of Differential Geometry, 2023, arXiv:1802.01534) ♦ Invariance of symplectic cohomology and twisted cotangent bundles over surfaces (joint with G. Benedetti) (Internat. J. Math. 2020) ♦ The monotone wrapped Fukaya category and the open-closed string map (joint with I. Smith) (Selecta 2017) ♦ Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties (Geom & Topol 2016) ♦ Floer theory for negative line bundles via Gromov-Witten invariants (Adv Math 2014) ♦ Topological quantum field theory structure on symplectic cohomology (J Topol 2013) ♦ Deformations of symplectic cohomology and exact Lagrangians in ALE spaces (GAFA 2010) ♦ Novikov-symplectic cohomology and exact Lagrangian embeddings (Geom & Topol 2009) Lecture notes  ⋄ Algebraic Topology : Lecture notes here. ⋄ Algebraic Geometry : Lecture notes here. ⋄ Introduction to Schemes : Lecture notes here. ⋄ Lie Groups : Lecture notes here. ⋄ Geometry of Surfaces : Lecture notes here. ⋄ Morse Homology (Graduate course) : Lecture notes here.   (Also: old Cambridge Part III Lecture notes: here). ⋄ Geometry, Topology, Penrose Tilings: Oxford Masterclasses 2014. ⋄ Talk on Penrose tilings: Wadham College Maths Reunion 2015. Slides of Talks  ⋄ Slides of a lecture series from 2021: Symplectic Topology Slides. Links  Italian poetry ___________________________ Link to my departmental webpage Link to my contact details: here. Alexander F. Ritter. Professor of Mathematics, Mathematical Institute, Oxford. The Roger Penrose Fellow and Tutor, Wadham College, Oxford.