Universität Hamburg
Fachbereich Mathematik
Geomatikum Raum 420

Sprechstunde / consultation hours: nach Vereinbarung / by appointment

Research

Research Interests

Integrable and (conformally) superintegrable Hamiltonian systems on manifolds, Mathematical General Relativity

Overdetermined finite-type PDE systems

Riemannian and pseudo-Riemannian geometry, conformal and Weylian structures

Projective Differential Geometry, (pseudo-)Riemannian metrics with projective symmetries

Affine hypersurfaces, Information Geometry, Hessian geometry, statistical manifolds

Frobenius Manifolds and the Witten-Dijkgraaf-Verlinde-Verlinde Equation

Publications

Preprints

• Affine hypersurfaces and superintegrable systems (with Vicente Cortés), 7 Apr 2025, preprint: arXiv:2504.05200

• A necessary and sufficient condition for a second-order superintegrable system with (n+1)-parameter potential to extend to a non-degenerate second-order superintegrable system (with J. Nugent), 11 Nov 2024, preprint: arXiv:2411.06994

• Superintegrable systems on conformal surfaces (with J. Kress, K. Schöbel), 14 March 2024, preprint: arXiv:2403.09191

Accepted for Publication

• Manifolds with a Commutative and Associative Product Structure that Encodes Superintegrable Hamiltonian Systems, Ann. Henri Poincaré (2025), available online: https://link.springer.com/article/10.1007/s00023-025-01608-5

• Second-order superintegrable systems and Weylian geometry, 1 Nov 2024, preprint: arXiv:2411.00569, to appear in Nuclear Physics B, in press, Pre-proof available online (26 August 2025), 117095, https://doi.org/10.1016/j.nuclphysb.2025.117095

• On dual-projectively equivalent connections associated to second order superintegrable systems,  27 Dec 2024, preprint: arXiv:2412.19739, accepted for publication in Arnold mathematical Journal (2025-05-30)

• On Haantjes tensors for second-order superintegrable systems (with Ian Marquette, Damien McLeod and Serena Scapucci), 17 Dec 2024, preprint: arXiv:2412.13007, accepted by MATRIX Ann.

• Projective Differential Geometry of Geodesics, and Integrable Systems (with G. Manno and J. Schumm), accepted for publication by Rend. Sem. Mat. Univ. Pol. Torino.

Journal Papers

• Abundant Superintegrable Systems and Hessian Structures (with John Armstrong), 8 Oct 2024, preprint: arXiv:2410.05009, Journal of Geometry and Physics 214, 105503 (2025), doi:10.1016/j.geomphys.2025.105503)

• The c-projective symmetry algebras of Kähler surfaces (with G. Manno, J. Schumm), The Journal of Geometric Analysis 35, number 75 (2025), preprint: arXiv:2209.11301, doi: 10.1007/s12220-024-01878-1

• Torsion-free connections of second-order maximally superintegrable systems, 13 March 2024, preprint: arXiv:2403.08509, Bull. London Math. Soc. 57, issue 2 (2025), first published online 24 Dec 2024, doi: http://doi.org/10.1112/blms.13213

• Algebraic Conditions for Conformal Superintegrability in Arbitrary Dimension (with Jonathan Kress and Konrad Schöbel),  Communications in Mathematical Physics 405, article number 92, 2024 (online 20 march 2024), preprint: arXiv:2006.15696

• An Algebraic Geometric Foundation for a Classification of Superintegrable Systems in Arbitrary Dimension (with Jonathan Kress and Konrad Schöbel), Journal of Geometric Analysis 33, no. 360 (2023), doi:10.1007/s12220-023-01413-8

• 3-dimensional Levi-Civita metrics with projective vector fields (with Gianni Manno), Journal de Mathématiques Pures et Appliquées 163 (2022), pp. 473–517 (available online since 18 May 2022), doi:10.1016/j.matpur.2022.05.012

• Stäckel Equivalence of Non-Degenerate Superintegrable Systems, and Invariant Quadrics,  SIGMA 17 (2021), 015, 13 pages, arXiv:2010.03638, doi:10.3842/SIGMA.2021.015

• Normal forms of two-dimensional metrics admitting exactly one essential projective vector field (with Gianni Manno),
  preprint arXiv.org:1705.06630, Journal de Mathématiques Pures et Appliquées, Volume 135, March 2020, Pages 26-82, doi:10.1016/j.matpur.2020.01.003

• Projectively equivalent 2-dimensional superintegrable systems with projective symmetries, arXiv.org:1812.03591, Journal of Physics A: Mathematical and Theoretical, Volume 53, Number 9 (Published 10 February 2020), doi:10.1088/1751-8121/ab6fc5

• (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry (with Gianni Manno), Journal of Geometry and Physics 145 (Nov 2019), 103476, doi: https://doi.org/10.1016/j.geomphys.2019.07.007

• Benenti Tensors: A useful tool in Projective Differential Geometry (with Gianni Manno), Complex Manifolds, Volume 5, Issue 1, 2018, Pages 111–121, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2018-0006

• On integrability of certain rank 2 sub-Riemannian structures (with Boris Kruglikov and Georgios Lukes-Gerakopoulos), G. Regul. Chaot. Dyn. (2017) 22: 502, doi:10.1134/S1560354717050033, preprint: arXiv:1507.03082

• Determining the number of Killing tensors by (linear) algebra, Note di Matematica Volume 37, suppl. 1 (2017), doi:10.1285/i15900932v37suppl1p187

• Killing tensors in stationary and axially symmetric space-times, Journal of Geometry and Physics, Volume 115, May 2017, Pages 28–36, doi: http://dx.doi.org/10.1016/j.geomphys.2016.09.009, preprint: arXiv:1602.08968

• Reducibility of valence-3 Killing tensors in Weyl's class of stationary and axially symmetric spacetimes, Phys. Rev. D 92, 084036 (2015), doi: 10.1103/PhysRevD.92.084036

Book Contributions / Conference Proceedings

• Metrics admitting projective and c-projective vector fields (with Gianni Manno and Jan Schumm), chapter within the AMS Contemporary Mathematics (volume 788) book “The Diverse World of PDEs:Geometry and Mathematical Physics” (edited by I. S. Krasil’shchik, A. B. Sossinsky and A. M. Verbovetsky), 2023, ISBN: 978-1-4704-7147-7.

Thesis

• First integrals in stationary and axially symmetric space-times and sub-Riemannian structure, Faculty of Mathematics and Computer Science, Friedrich Schiller University Jena, Germany (March 2016)

Work

10/2022 - present: Department of Mathematics, Universität Hamburg

• Wissenschaftlicher Mitarbeiter (Research Associate) within the Section Analysis & Differential Geometry

10/2020 - 09/2022: DISMA, Politecnico di Torino

• Assegnista di Ricerca (Research Fellow)

05/2020-09/2020: DFG Return Fellow, Stuttgart University

• Return (Repatriation) Fellowship granted by Deutsche Forschungsgemeinschaft (German Research Foundation)

• Research visitor at the Institute of Geometry and Topology, University of Stuttgart (Germany)

04/2018-03/2020: DFG Research Fellow, UNSW Sydney

• Research Fellow of Deutsche Forschungsgemeinschaft (German Research Foundation, project number 353063958). 

• Visiting Fellow at the School of Mathematics and Statistics, University of New South Wales (Sydney, Australia), until 04/2020

04/2016-03/2018: Research Fellow of Istituto Nazionale di Alta Matematica (INdAM)

• Fellowship by Istituto Nazionale di Alta Matematica "F. Severi", Rome.

• Politecnico di Torino (Turin, Italy), Project FIR-2013 Geometria delle equazioni differenziali,

• Member of Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of INdAM.

11/2012-03/2016: PhD student and Research Assistant at FSU Jena

• PhD student and Research Assistant at Friedrich Schiller University Jena, Department for Mathematics, Faculty of Mathematics and Computer Sciences / Research Training Group Quantum and Gravitational Fields (funded by Deutsche Forschungsgemeinschaft)

• Supervisor: Vladimir S. Matveev

Reviewer for Zentralblatt zbMath Open (since Jan 2022)

Reviewer for MathSciNet / Mathematical Reviews (since Oct 2018)

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