Miguel Moreira

Hello! My name is Miguel and this is my webpage. Since 2026 I am an Assistant Researcher at Instituto Superior Técnico (IST Lisbon), associated with CAMGSD. Before I was a Moore instructor at MIT (2023-26), supervised by Davesh Maulik, and before that I was a PhD student at ETH Zurich (2019-23), advised by Rahul Pandharipande.

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

Contacts

Email: miguel.moreira(at)tecnico.ulisboa.pt

Address: Instituto Superior Técnico, Departamento de Matemática, Avenida Rovisco Pais, 1049-001 Lisboa

Office: 5.16

Papers and preprints

• Rationality and symmetry of stable pairs generating series for Fano 3-folds [2026] (joint with I. Karpov).
• Generalized K-theoretic invariants and wall-crossing via non-abelian localization [2025] (joint with I. Karpov).
• On the intersection theory of moduli spaces of parabolic bundles [2025].
• Higher range asymptotic formulas for (refined) Poincaré polynomials, appendix for the paper Poincaré polynomials of moduli spaces of one-dimensional sheaves on the projective plane by S. Guo and L. Wu [2025].
• On the Chern filtration for the moduli of bundles on curves [2024] (joint with W. Lim and W. Pi).
• Virasoro constraints and representations for quiver moduli spaces [2024] (joint with W. Lim), to appear in Algebraic Geometry.
• 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 ℙ² [2023] (joint with W. Lim and W. Pi), published in Forum of Mathematics, sigma (2024). 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], published in Journal of Algebraic Geometry (2024).
• 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).

Slides and notes from talks

• Rationality and symmetry of stable pairs generating series for Fano 3-folds, slides for VBAC webinar (2026).
• Enumerative geometry and Virasoro constraints, slides for colloquium talk at UMass Boston (2025).
• Intersection theory on moduli of parabolic bundles, video of talk in the Geometria em Lisboa seminar at Instituto Superior Técnico (2025).
• Chern filtrations for 1-dimensional sheaves and bundles, notes for in person talk in the Informal Mathematical Physics Seminar at Columbia (2024).
• Virasoro constraints, video of talk in Enumerative Invariants, Quantum Fields and String Theory Correspondences workshop at Mittag-Leffler (2024).
• 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). Video here.
• 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)

Teaching

• MIT: Multivariable calculus (18.022, Fall 25).
• MIT: Commutative Algebra (18.705, Fall 24). Some course material can be found here.
• Recitations at MIT: Multivariable calculus (18.702, Fall 23), differential equations (18.703, Spring 24 and Spring 25).
• Exercise classes at ETH: Topology (Spring 20), Algebra II (Spring 21).

Some notes

• 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).