Math
I worked in the field of Symplectic Geometry, more specifically symplectic capacities.
PhD Thesis
- Equivariant symplectic homology, linearized contact homology and the Lagrangian capacity
Advisor: Kai Cieliebak
Grade: Summa Cum Laude
Publications
- J. Gutt, M. Pereira, and V. Ramos. Cube normalized symplectic capacities. arXiv:2208.13666 [math.SG], Aug. 2022
- M. Pereira. On the Lagrangian capacity of convex or concave toric domains. arXiv:2207.11022 [math.SG], July 2022
- J. Mourão, J. Nunes, and M. Pereira. Partial coherent state transforms, $G \times T$-invariant Kähler structures and geometric quantization of cotangent bundles of compact Lie groups. Advances in Mathematics, 368:107139, July 2020
Teaching
I was a tutor for the following courses at the University of Augsburg:
- 2020-2021 (Winter). Riemannian geometry (exercise sheets)
- 2019-2020 (Summer). Topology (exercise sheets)
- 2018-2019 (Summer). Holomorphic curves (exercise sheets)
- 2017-2018 (Summer). Topology
Talks
- 2022-06-07. The Lagrangian capacity of toric domains, at the Institute of Mathematics of Toulouse (slides)
- 2022-05-27. The Lagrangian capacity of toric domains, at the CRM-Montréal/Princeton-IAS/Tel Aviv/Paris joint seminar (slides, video)
- 2022-04-19. The Lagrangian capacity of toric domains, at Instituto Superior Técnico/Geometria em Lisboa seminar (slides, video)
- 2021-11-05. $S^1$-equivariant symplectic homology and symplectic capacities, at the Korea Institute for Advanced Study (slides)
- 2021-04-27. Stops, at the Berlin-Hamburg-Augsburg Symplectic Seminar (slides)
- 2021-04-26. Symplectic capacities part 2, at the University of Augsburg Geometry and Topology group seminar (slides)
- 2020-11-24. Bi-Hamiltonian mechanical systems, at the University of Augsburg Symplectic Seminar (slides)
- 2020-11-23. Symplectic capacities, at the University of Augsburg Geometry and Topology group seminar (slides)
- 2020-05-18. Geometric quantization of the cotangent bundle of a Lie group, at the University of Augsburg Oberseminar (slides)