Hello! My name is Miguel and this is my webpage. Since 2023 I am a Moore instructor at MIT, supervised by Davesh Maulik. Before I was a PhD student at ETH Zurich and my advisor was Rahul Pandharipande. Even before that I did my bachelor and master in Instituto Superior Técnico, Lisbon. My master's thesis advisors were Miguel Abreu and Leonardo Macarini.

My research mostly concerns enumerative invariants and moduli spaces parametrizing some sort of geometric objects (such as sheaves, curves or quiver representations).

**Email:** miguel(at)mit.edu

**Address:** MIT Department of Mathematics, 182 Memorial Dr, Cambridge, MA 02139

**Office:** 2-155

- Virasoro constraints and representations for quiver moduli spaces [2024] (joint with W. Lim).
- Cohomology rings of the moduli of one-dimensional sheaves on the projective plane [2024] (joint with Y. Kononov, W. Lim and W. Pi). The cohomology rings that we computed can be found here.
- Cohomological χ-dependence of ring structure for moduli of 1-dimensional sheaves on ℙ
^{2}[2023] (joint with W. Lim and W. Pi), to appear in Forum of Mathematics, sigma. See also code and pdf print. - Virasoro constraints on moduli of sheaves and vertex algebras [2022] (joint with A. Bojko and W. Lim), published in Inventiones Mathematicae (2024).
- Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology [2022] (joint with M. Abreu and L. Macarini), published in Advances in Mathematics (2023).
- Weyl symmetry for curve counting invariants via spherical twists (joint with T. Buelles) [2021], to appear in Journal of Algebraic Geometry.
- Virasoro constraints for Hilbert scheme of points and for the cubic 3-fold [2020], published in Journal of the London Mathematical Society (2022).
- Virasoro constraints for stable pairs on toric 3-folds [2020] (joint with A. Oblomkov, A. Okounkov and R. Pandharipande), published in Forum of Mathematics, Pi (2022).
- On contact invariants of non-simply connected Gorenstein toric contact manifolds [2018] (joint with M. Abreu and L. Macarini), published in Mathematical Research Letters (2022).
- On representations of Cuntz algebras and pure isometries (joint with A. Boussejra and P. Pinto) [2016], published in Journal of Mathematical Analysis and Applications (2017).
- Local conjugacy of irreducible hyperbolic toral automorphisms (joint with L. Bakker and P. M. Rodrigues) [2016], preprint.
- The 123 theorem of Probability Theory and Copositive Matrices (joint with A. Kovačec and D. Martins) [2013], published in Spec. Matrices (2014).

- CoHA and Hecke operators on surfaces, extended abstract for talk at the Oberwolfach workshop on P=W, following the paper by Mellit-Minets-Schiffmann-Vasserot.
- The cohomology ring of moduli of 1-dimensional sheaves, slides for talk at the Intercontinental Moduli Zoominar (2024).
- PhD defense talk (2023).
- The cohomology ring is not χ-independent, notes for in person talk in ETH moduli seminar (2023).
- Virasoro constraints on sheaf moduli spaces via wall-crossing, M-seminar, Kansas State University (2023).
- Virasoro constraints: vertex algebra and wall-crossing, notes for in person talk in the Simons Collaboration meeting, Oxford (2022). Woonam gave a first talk on the subject.
- Virasoro constraints on sheaf moduli spaces via wall-crossing, Geometria em Lisboa (2022).
- Virtual fundamental classes, after Behrend Fantechi, notes for in person talk in DT Aussois (2022).
- Virasoro constraints on sheaf moduli spaces via wall-crossing, Algebraic Geometry Seminar, University of Chicago Illinois (2022).
- Virasoro constraints for stable bundles on curves, notes for in person talk in Diablerets, Helvetic Algebraic Geometry Seminar (2022). Arkadij gave a second talk.
- Weyl symmetry, Enumerative Geometry Seminar, YMSC - Tsinghua University (2022) and Mathematical Physics seminar, Harvard-MIT (2021).
- The Gromov-Witten/Stable pairs correspondence, Encontro Nacional da Sociedade Portuguesa de Matemática (2021).
- Enumerative theory of local Hirzebruch surfaces via the topological vertex, ETH Moduli Zoominar (2021).
- Virasoro for stable pairs, ETH Moduli Zoominar (2020) and Mathematical Physics seminar, Harvard (2021)

- Will participate in the workshop Enumerative Invariants, Quantum Fields and String Theory Correspondences, July 22-26, Mittag-Leffler institute.

- Floer homology for global quotient orbifolds, Master's Thesis at Instituto Superior Técnico, supervised by Miguel Abreu and Leonardo Macarini (2019). You can also read the extended abstract.
- Thom cobordism theorem, project for a Homotopy Theory course lectured by Pedro Boavida (2019).
- The Flux homomorphism, project for a Symplectic Geometry course lectured by Leonardo Macarini (2018).
- On Lie's third theorem, project for a Lie Groups and Lie Algebras course lectured by Gustavo Granja (2018).
- Riemann surfaces and modular functions, final bachelor project at Instituto Superior Técnico, supervised by Gustavo Granja (2017).
- Some notes on Euclidean Geometry of olympic flavour, joint with Nuno Arala (in Portuguese): Geometry for begginers, Power of a point, Random configurations and Brute Force (2014).