Submitted Preprints

  1. Extending compact Hamiltonian S1-spaces to integrable systems with mild degeneracies in dimension four (with J. Palmer), preprint version, 51p., arXiv:2105.00523.

Publications

  1. A family of semitoric systems with four focus-focus singularities and two double pinched tori (with A. De Meulenaere), 50p., to appear in Journal of Nonlinear Science, arXiv:1911.11883 [math.DS].
  2. The height invariant of a four-parameter semitoric system with two focus-focus singularities (with J. Alonso), 32p., Journal of Nonlinear Science (2021) 31:51, arXiv:2006.15369 [math.DS].
  3. Characterization of toric systems via transport costs, Journal of Geometric Mechanics, Volume 12, Number 3, September 2020, pp. 447-454; arXiv:1909.06902 [math.SG].

  4. The Symplectic Fueter-Sce Theorem (with D. Eelbode and G. Muarem), Adv. Appl. Clifford Algebras 30, 49 (2020); arXiv:1909.09686 [math.SG].

  5. Survey on recent developments in semitoric systems (with J. Alonso), Conference Proceedings of RIMS Kokyuroku 2019 (Research Institute for Mathematical Sciences, Kyoto University, Japan, journal identifier ISSN 1880-2818), no. 2137, 15p., arXiv:1901.10433 [mathDS].

  6. Symplectic classification of coupled angular momenta (with J. Alonso and H. Dullin), Nonlinearity 33 (2020), 417-468. Preprint version via arXiv:1808.05849 [mathDS], 59p.

  7. Taylor series and twisting-index invariants of coupled spin-oscillators (with J. Alonso and H. Dullin), Journal of Geometry and Physics, Volume 140 (2019), 131-151. Preprint version (pdf, 2,6 MB), 38p.

  8. Faithful semi-toric systems (with S. Sabatini, D. Sepe, M. Symington), Symmetry, Integrability, and Geometry: Methods and Applications (SIGMA) 14 (2018), 084, 66p., former titel/version: Vertical almost toric systems, 72p.

  9. A family of compact semitoric systems with two focus-focus singularities (with J. Palmer), Journal of Geometric Mechanics 2018, 10(3): 331–357, Preprint version (pdf, 5 MB), 27p., arXiv:1710.05746 [math.SG].

  10. Computational complexity, torsion-freeness of homoclinic Floer homology and homoclinic Morse inequalities, Nonlinearity 30 (2017), 2547–2565. Preprint version (pdf, 356 KB).

  11. Optimal transport and integer partitions, Discrete Applied Mathematics 190/191 (2015), 75–85. Preprint version (pdf, 166 KB).

  12. Hyperkähler Floer theory as infinite dimensional Hamiltonian system, Proc. Amer. Math. Soc. 143 (2015), no. 8, 3519–3524. Preprint version (pdf, 253 KB).

  13. From compact semi-toric systems to Hamiltonian S^1-spaces (with S. Sabatini, D. Sepe), Discrete Contin. Dyn. Syst. 35 (2015), no. 1, 247–281. Preprint version (pdf, 521 KB).

  14. Higher Morse moduli spaces and n-categories. Homology Homotopy Appl. 16 (2014), no. 2, 1–32. Preprint version (pdf, 550 KB).

  15. On the image of the almost strict Morse N-category under almost strict N-functors. Theory Appl. Categ. 29 (2014), No. 3, 21–47. Preprint version (pdf, 377 KB).

  16. Homoclinic points and Floer homology. J. Symplectic Geom. 11 (2013), no. 4, 645–701. Preprint version (pdf, 805 KB).

  17. Transport, flux and growth of homoclinic Floer homology. Discrete Contin. Dyn. Syst. 32 (2012), no. 10, 3587–3620. Preprint version (pdf, 647 KB).

  18. Floer homology groups in hyperkähler geometry (with G. Noetzel, D. Salamon). New perspectives and challenges in symplectic field theory, 251–261, CRM Proc. Lecture Notes, 49, Amer. Math. Soc., Providence, RI, 2009. Preprint version (pdf, 143 KB).

  19. Hypercontact structures and Floer homology (with G. Noetzel, D. Salamon). Geom. Topol. 13 (2009), no. 5, 2543–2617. Preprint version (pdf, 468 KB).

 

Lecture Notes

 

  1. Calculus voor Informatici, iv+117p., University of Antwerp, Spring term 2017.
  2. Multivariate calculus, iii+117p.,  University of Antwerp, Spring term 2017.
  3. Gewone differentiaalvergelijkingen en dynamische systemen, iv+129p., University of Antwerp, Autumn term 2020.
  4. Geometric Functional Analysis, ii+75p., University of Antwerp, Autumn term 2017.
  5. Integrable Hamiltonian systems, ii+105p., University of Antwerp, Autumn term 2018.
  6. Selected aspects of the Korteweg-de Vries equation, ii+54p., University of Antwerp, Spring term 2020.

Habilitation thesis, PhD thesis, and Diploma thesis

  1. From Floer theory in symplectic and hyperkähler geometry via integrable Hamiltonian systems and Morse theory and n-category theory to optimal mass transport and integer partitions, Habilitation thesis, Université de Franche-Comté (Besançon) 2014, 56p.
  2. Floer homology for homoclinic tangles, Dissertation, 153 p., University of Leipzig 2008 (Advisor: Prof. M. Schwarz).
  3. Optimal mass transportation in the Monge-Kantorovich transport problem (German), Diploma thesis 2003, 60 p., University of Freiburg i.Br. (Advisor: Prof. V. Bangert).

Oberwolfach Reports

  1. Dynamics near focus-focus singular fibres in semitoric systems, Oberwolfach Report No. 32/2017, DOI: 10.4171/OWR/2017/32.
  2. From semi-toric systems to Hamiltonian S^1-actions and back, Oberwolfach Report No. 34/2015, 1964 -- 1966, DOI: 10.4171/OWR/2015/34.
  3. Dynamical aspects of homoclinic Floer homology, Oberwolfach Reports, Volume 8, Issue 3 (2011), 1933 -- 1935.
  4. Floer homology for homoclinic tangles, Oberwolfach Reports, Volume 5, Issue 3 (2008), 2354 -- 2356.

MathSciNet Reviews

I have written 44 reviews for MathSciNet (state of the art in April 2019). If you have a MathSciNet subscription you may find them HERE.

Various notes, preprints, surveys