Alexander Ritter

Alexander Ritter is a Professor of Mathematics at the University of Oxford, affiliated with the Mathematical Institute and Wadham College. Holding a PhD from MIT (2009), he maintains active research and teaching roles, including Michaelmas 2025 Linear Algebra instruction.

Education

• PhD, Massachusetts Institute of Technology (MIT), 2009

Research Focus

Professor Ritter specializes in symplectic topology, homological mirror symmetry, Floer theory, and Gromov-Witten theory. His work bridges symplectic geometry with algebraic geometry through quantum cohomology invariants, Fukaya categories, and spectral sequence techniques. Key innovations include filtrations on quantum cohomology using C*-actions and Morse-Bott-Floer theory to analyze semiprojective toric manifolds and singularities.

Publication Evolution

Recent publications (2023-2025) reveal intensified collaboration with Filip Živanović on quantum cohomology filtrations, yielding eight joint papers. This work integrates Hilbert-Poincaré series, equivariant cohomology, and McKay correspondence applications, demonstrating progression from foundational symplectic cohomology (2009-2013) toward geometric topology and birational geometry implications.

Honors and Recognition

• Junior Research Fellowship, Trinity College, Cambridge (2009-2013)
• Research Fellowship, MIT (2007-2008)
• McCormick Fellowship, University of Chicago (2004-2006)
• Rouse Ball Prize & Heilbronn Prize, Trinity College, Cambridge (2003)
• Senior/Junior Scholarships, Trinity College, Cambridge (2001-2002, 2023)

Research Funding

As Principal Investigator for EPSRC grant EP/Z535977/1 (2025-2028; £806K), he leads research on "Orbifold Floer cohomology and birational geometry." Previously, he served as Co-Investigator with Dominic Joyce on EPSRC grant EP/T012749/1 (2019; £653K) exploring Bridgeland stability in Fukaya categories of Calabi–Yau 2–folds.

Academic Environment

Based in Oxford's Geometry research group, Ritter collaborates extensively within symplectic topology networks. His 2022-2023 Visiting Associate Professorship at Stanford University underscores international recognition, while consistent teaching of advanced courses (e.g., Morse homology, Algebraic Topology) reflects commitment to graduate education.