Hello! My name is Miguel and this is my webpage.
Since 2019 I'm a PhD student at ETH Zurich and my advisor is Rahul Pandharipande.
Before that I did my bachelor's degree (finished in 2017) and master's degree (finished in 2019) in Instituto Superior Técnico, Lisbon.
My master's thesis advisors were Miguel Abreu and Leonardo Macarini.
My research mostly concerns enumerative invariants defined using moduli spaces parametrizing some sort of geometric objects. Examples include Gromov-Witten theory, stable pairs, Hilbert schemes or moduli of stable bundles. Lately I've been particularly interested in formulating and understanding the Virasoro constraints on different moduli spaces of sheaf-like objects.
Address: ETH Zurich, Rämistrasse 101, 8092 Zurich
Office: HG J16.1
Papers and preprints
- Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology  (joint with M. Abreu and L. Macarini), preprint.
- Weyl symmetry for curve counting invariants via spherical twists (joint with T. Buelles) , preprint.
- Virasoro constraints for Hilbert scheme of points and for the cubic 3-fold , to appear in Journal of the London Mathematical Society (2021).
- Virasoro constraints for stable pairs on toric 3-folds  (joint with A. Oblomkov, A. Okounkov and R. Pandharipande), to appear in Forum of Mathematics, Pi.
- On contact invariants of non-simply connected Gorenstein toric contact manifolds  (joint with M. Abreu and L. Macarini), to appear in Mathematical Research Letters.
- On representations of Cuntz algebras and pure isometries (joint with A. Boussejra and P. Pinto) , published in Journal of Mathematical Analysis and Applications (2017).
- Local conjugacy of irreducible hyperbolic toral automorphisms (joint with L. Bakker and P. M. Rodrigues) , preprint.
- The 123 theorem of Probability Theory and Copositive Matrices (joint with A. Kovačec and D. Martins) , published in Spec. Matrices (2014).
Slides from talks
Some notes, reports for courses, projects and others
The notes here (with the exception of the master thesis) are expository and I claim no originality (nor lack of typos).
- 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).
Last updated 07/02/2022