Homologia de Contato Mergulhada (ECH) e seus invariantes espectrais. Lei de Weyl em ECH. Closing Lemma de Asaoka-Irie.
Homologia de Floer Periódica (PFH), invariantes espectrais e sua lei de Weyl. Closing lemma para difeomorfismos hamiltonianos em superfícies. Tópicos adicionais: Equidistribuição de órbitas de Reeb, Simplicity conjecture.

Referências:
1) Michael Hutchings, Lecture notes on embedded contact homology, in Contact and Symplectic Topology, Frédéric Bourgeois, Vincent Colin, and András Stipsicz, eds., Bolyai Society Mathematical Studies 26, Springer, 2014, pp. 389–484. arXiv:1303.5789. doi:10.1007/978-3-319-02036-5_9.
2) Daniel Cristofaro-Gardiner, Michael Hutchings, and Vinicius Gripp Barros Ramos, The asymptotics of ECH capacities, Inventiones Mathematicae 199 (2015), no. 1, 187–214. arXiv:1210.2167. doi:10.1007/s00222-014-0510-7.
3) Masayuki Asaoka and Kei Irie, A C∞ closing lemma for Hamiltonian diffeomorphisms of closed surfaces, Geometric and Functional Analysis 26 (2016), no. 5, 1245–1254. arXiv:1512.06336. doi:10.1007/s00039-016-0386-3.
4) Daniel Cristofaro-Gardiner, Vincent Humilière, and Sobhan Seyfaddini, PFH spectral invariants on the two-sphere and the large scale geometry of Hofer’s metric, Journal of the European Mathematical Society 26 (2024), no. 12, 4537–4584. arXiv:2102.04404. doi:10.4171/JEMS/1351.
5) Oliver Edtmair and Michael Hutchings, PFH spectral invariants and C∞ closing lemmas, preprint, arXiv:2110.02463, 2021.
6) Daniel Cristofaro-Gardiner, Vincent Humilière, and Sobhan Seyfaddini, Proof of the simplicity conjecture, Annals of Mathematics (2) 199 (2024), no. 1, 181–257. arXiv:2001.01792. doi:10.4007/annals.2024.199.1.3.