Research interests:

• My research encompasses problems that show connections between symplectic geometry and practical problems in Hamiltonian dynamical systems, with a particular focus on the restricted three-body problem. I am keenly interested in the interaction between the Conley–Zehnder index and bifurcations of periodic orbits, performing both theoretical and numerical studies.
  Why? At bifurcation points the index jumps. When working locally near a family of non-degenerate periodic orbits, there is a fascinating bifurcation-invariant: the local Floer homology and thus its Euler characteristic. Since the index leads to a grading on local Floer homology, the index provides important information how different families are related to each other before and after bifurcation. This helps to deduce connections that are hard to see by pure computations.

• An additional research area includes symplectic embedding problems, especially using ECH capacities for embeddings of concave toric domains into convex toric domains.

• My goal is not only to solve concrete problems, but also to form a method pool capturing the key aspects of these problems and to build further bridges between symplectic tools and applied problems.

Publications

• Journal article

1. Bifurcation graphs for the CR3BP via symplectic methods (with Urs Frauenfelder, Otto van Koert, Dayung Koh, Agustin Moreno)
   Submitted for publication (2024)

2. From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices
   Journal of Mathematical Physics 64(8) (2023)
   https://doi.org/10.1063/5.0156959

3. Symplectic splitting of Hamiltonian structures and reduced monodromy matrices
   Linear Algebra and its Applications  674, 426–441 (2023)
   https://doi.org/10.1016/j.laa.2023.06.008

4. The Conley–Zehnder indices of the spatial Hill three-body problem
   Celestial Mechanics and Dynamical Astronomy 135(32) (2023)
   https://doi.org/10.1007/s10569-023-10134-7

5. The linear symmetries of Hill's lunar problem
   Archiv der Mathematik 120(3), 321–330 (2023)
   https://doi.org/10.1007/s00013-022-01822-1

• Conference paper
  Symplectic methods in space mission design (with Urs Frauenfelder, Dayung Koh, Agustin Moreno)
  To appear in the Proceedings of the 2023 AAS/AIAA Astrodynamics Specialist Conference
  https://arxiv.org/abs/2308.03391v1

• Doctoral thesis
  A study of the Hill three-body problem by modern symplectic geometry
  Université de Neuchâtel, No de thèse: 3063 (2023)
  https://doi.org/10.35662/unine-thesis-3063

My ORCID profile

ResearchGate profile

Google Scholar profile

arXiv page

Scientific collaborators

• Alexander Batkhin, Technion, Israel Institute of Technology, Israel

• Urs Frauenfelder, Universität Augsburg, Germany

• Otto van Koert, Seoul National University, South Korea

• Dayung Koh, JPL, NASA, Pasadena, California, USA

• Bhanu Kumar, JPL, NASA, Pasadena, California, USA / Universität Heidelberg, Germany

• Agustin Moreno, Universität Heidelberg, Germany

• Felix Schlenk, Université de Neuchâtel, Switzerland

Ongoing projects / in progress

• A study of the Earth–Moon problem from a symplectic point of view: Bifurcation graphs and Conley–Zehnder indices

• On Lyapunov, halo and polar orbits in the Hill three-body problem

• On symplectic embeddings for the rotating Kepler problem

• Symplectic embeddings for axial simplices and Lp-balls. Joint with Felix Schlenk

Participation in conferences / workshops / summer schools

• Symplectic Dynamics in Aachen | RWTH Aachen, Sept. 16-20, 2024

• Theories of the three-body system | Monash University Prato Centre, Sept. 8-13, 2024

• Symplectic Geometry and Anosov Flows | Internationales Wissenschaftsforum Heidelberg, July 22-26, 2024

• 29th International Symposium on Space Flight Dynamics (ISSFD 2024) | Europäisches Raumflugkontrollzentrum (ESOC), Darmstadt, April 22-26, 2024

• CAST 2024 | Ruhr-Universität Bochum, Febr. 8-10, 2024

• Strasbourg-Heidelberg "Symplectic Day" | IRMA Strasbourg, Nov. 16, 2023

• Geometry and Dynamics. A Conference in Honour of Leonid Polterovich | ETH Zürich, June 26-30, 2023

• Two days in Symplectic Dynamics | École normale supérieure de Lyon, Sept. 29-30, 2022

• Online Miniworkshop on Symplectic and Contact Dynamics | Funded by the University of Antwerp, May 12, 2021

• Conservative Dynamics and its Interactions | École Polytechnique Fédérale de Lausanne, Aug. 19-30, 2019

• Conference in honor of Prof. André Haefliger's 90th birthday | Université de Genève, May 15-17, 2019

• Workshop on Symplectic Field Theory IX | Universität Augsburg, Aug. 25-31, 2018

Talks

• "On Babylonian lunar periods and Conley–Zehnder indices of the CR3BP"
  Nov. 8, 2023 | Symplectic Geometry Seminar, Universität Heidelberg