Prof. Alexander Ritter

PhD (MIT 2009)

Status

Academic Faculty

Associate Professor in Geometry

The Roger Penrose Fellow and Tutor in Mathematics, Wadham College

2022-2023 on sabbatical leave at Stanford

+44 1865 273556

Contact form

http://people.maths.ox.ac.uk/ritter/

ORCID iD

https://orcid.org/0000-0001-8286-7887

Research groups

Geometry

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

Quantum cohomology and Floer invariants of semiprojective toric manifolds, arXiv:2501.09011, 2025 (joint w/ Filip Živanović)

Filtrations on equivariant quantum cohomology and Hilbert-Poincaré series, arXiv:2410.17237, 2024 (joint w/ Filip Živanović)

Filtrations on quantum cohomology via Morse-Bott-Floer Spectral Sequences, arXiv:2304.14384v3, 2023 (joint w/ Filip Živanović)

Filtrations on quantum cohomology from the Floer theory of C∗-actions, arXiv:2304.13026v4, 2023 (joint w/ Filip Živanović)

The McKay correspondence for isolated singularities via Floer theory, Journal of Differential Geometry, 2023 (joint w/ Mark McLean)

Invariance of symplectic cohomology and twisted cotangent bundles over surfaces, International Journal of Mathematics, 2020 (joint w/ Gabriele Benedetti)

The monotone wrapped Fukaya category and the open-closed string map, Selecta Mathematica, 2017 (joint w/ Ivan Smith).

Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties, Geometry and Topology, 2016.

Floer theory for negative line bundles via Gromov-Witten invariants, Advances in Mathematics, 2014.

Topological quantum field theory structure on symplectic cohomology, Journal of Topology, 2013.

Deformations of symplectic cohomology and exact Lagrangians in ALE spaces, GAFA, 2010.

Novikov-symplectic cohomology and exact Lagrangian embeddings, Geometry & Topology, 2009.

Research interests

Symplectic topology, Homological Mirror Symmetry, Floer theory, Gromov-Witten theory.

Teaching

MT2024: M2: Analysis I - Sequences and Series
MT2024: A0: Linear Algebra
HT2024: TCC: Morse homology, with a view towards Floer theory
MT2023: M2: Analysis I - Sequences and Series
HT2022: C2.6 Introduction to Schemes
MT2021: C3.1 Algebraic Topology
HT2021: C2.6 Introduction to Schemes
MT2020: C3.1 Algebraic Topology
HT2020: C2.6 Introduction to Schemes
MT2019: C3.1 Algebraic Topology
MT2018: C3.4 Algebraic Geometry
MT2018: B3.2 Geometry of Surfaces
MT2017: C3.4 Algebraic Geometry
MT2017: B3.2 Geometry of Surfaces
MT2016: C3.4 Algebraic Geometry
MT2016: B3a Geometry of Surfaces
MT2015: C3.4 Algebraic Geometry
MT2015: B3a Geometry of Surfaces
HT2015: C3.4b Lie Groups
MT2014: B3a Geometry of Surfaces
Summer 2014: Lectures on Geometry, Topology, and Penrose Tilings (Oxford Masterclasses)
HT2014: C3.4b Lie Groups
MT2013: Graduate Course, Morse Homology
HT2013: C3.4b Lie Groups

Preferred address

Wadham College, Parks Road, Oxford OX1 3PN, England.

Prizes, awards, and scholarships

2025-2028 Principal Investigator, EPSRC standard grant EP/Z535977/1: £806K, 3-year grant, Orbifold Floer cohomology and birational geometry

2022-2023 Visiting Associate Professor of Mathematics, Stanford University

2019 Co-Investigator, EPSRC standard grant EP/T012749/1: £653K, 3-year grant, PI: Dominic Joyce, Co-Investigator: Jason Lotay. Bridgeland stability on Fukaya categories of Calabi–Yau 2–folds

2009-2013 Junior Research Fellowship, Trinity College, Cambridge.
2007-2008 Research Fellowship, MIT.
2004-2006 McCormick Fellowship, University of Chicago.
2003 Rouse Ball Prize, Trinity College, Cambridge.
2003 Heilbronn Prize, Trinity College, Cambridge.
2002, 2023 Senior Scholarship, Trinity College, Cambridge.
2001 Junior Scholarship, Trinity College, Cambridge.