Research interests
My research focuses on Algebraic Geometry with an emphasis on Gromov-Witten theory, logarithmic and tropical maps, moduli spaces of curves, and, more recently, moduli spaces of abelian varieties and Prym pairs.
Papers/Preprints
2024
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A. Cela, A.I. Lopez, The integral Chow ring of $\mathcal{R}_2$, preprint 2024
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A. Cela, A.U. Kumaran, and X.Yan (with an appendix by A. Aumonier), Chow ring of the stack of plane nodal curves, preprint 2024
2023
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A. Cela, A.I. Lopez, Genus 0 logarithmic and tropical fixed-domain counts for Hirzebruch surfaces, preprint 2023, published in J. London Math. Soc., 109: e12892 Journal version
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A. Cela, C. Lian, Fixed-domain curve counts for blow-ups of projective space, preprint 2023
2022
- A. Cela, Quantum Euler class and virtual Tevelev degrees of Fano complete intersections, preprint 2022, published in Arkiv för Matematik Journal version
2021
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A. Cela, C. Lian, Generalized Tevelev degrees of P1, preprint 2021, published in J. Pure Appl. Algebra Journal version
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A. Cela, R. Pandharipande and J. Schmitt, Tevelev degrees and Hurwitz moduli spaces, preprint 2021, published in Math. Proc. Cambridge Philos. Soc. Journal version
Notes
- Poster: Tevelev degrees presented in the conference 'Algebraic Geometry' in Roma Tre on the occasion of Sandro Verra's 70th birthday.
- Virtual fundamental classes These are notes I wrote during the seminars I and Miguel Moreira organised in HS 2021.
- Notes from a talk I gave about the paper Infinitesimal structure of the pluricanonical double ramification locus written by D. Holmes and J. Schmitt.
Old Thesis
- My Master Thesis: The virtual cohomological dimension of the Mapping Class Groups , supervised by Gabriele Mondello;
- My Bachelor Thesis (in Italian): Poincaré-Hopf Theorem for smooth manifolds, supervised by Paolo Piazza .
Talks given
- The integral Chow ring of R2, Zurich (ETHZ), Algebraic Geometry and Moduli Seminar, May 2024
- Fixed-curve counts in algebraic varieties, Seminario di Algebra and Geometria (La Sapienza University of Rome), April 2024
- Algebraic and tropical curves, Geometry Graduate Colloquium (ETHZ), October 2023
- What is ... Gromov-Witten Theory?, Zurich Graduate Colloquium (UZH), May 2023
- Fixed-domain curve counts for blow-ups of projective space, Lausanne (EPFL), March 2023
- Fixed-domain curve counts for blow-ups of projective space, Zurich (ETHZ), Algebraic Geometry and Moduli Seminar, March 2023
- Tevelev degrees, workshop 'Recent Advances on Moduli Spaces of Curves', March 2022
- Virtual Tevelev degrees and quantum Euler class of Fano complete intersections, Zurich (ETHZ), Algebraic Geometry and Moduli Seminar, March 2022
Math Travels
- 03/2024 : 'Enumerative Geometry and Arithmetic' at the Lorentz Center (Leiden)
- 02/2024 : 'A panorama of moduli spaces' in Goethe University Frankfurt am Main
- 07/2023 : 'AGNES Summer School on Intersection Theory on Moduli Spaces' in Brown University (Providence, RI)
- 06/2023 : 'Helvetic Algebraic Geometry Seminar' in Les Diablarets (Switzerland)
- 02/2023 : 'Moduli spaces: theory and coding' in Les Diablarets(Switzerland)
- 02/2023 : 'Logarithmic geometry & moduli spaces', in Goethe University Frankfurt
- 02/2023 : 'Northern German Algebraic Geometry Seminar and the award of the Algebraic Geometry Prize and the Compositio Prize', in HU Berlin
- 11/2022 : 'Resonance, topological invariance of groups and moduli' in HU Berlin
- 08/2022 : 'Tropical Geometry' in St. Mary's College, Moraga, California (organised by MSRI)
- 06/2022 : 'Algebraic Geometry' in Roma Tre on the occasion of Sandro Verra's 70th birthday (Italy)
- 06/2022 : 'Helvetic Algebraic Geometry Seminar' in Les Diablarets (Switzerland)
- 05/2022 : 'Curves and K3 surfaces' in Bonn (Germany)
- 03/2022 : 'Recent Advances on Moduli Spaces of Curves' in Leysin (Switzerland)
- 03/2022 : 'Admcycles: coding intersection theory' in Les Diablarets (Switzerland)
- 08/2021 : 'Helvetic Algebraic Geometry Seminar' in Geneva (Switzerland)
- 07/2019 : 'Perugia summer school' (SMI) in Perugia (Italy)