Carles Checa
PhD Researcher in Algebraic Geometry and Symbolic Computation
Hola! Hi! Χαίρετε! Ciao! I am a Ph.D. student at the National and Kapodistrian University of Athens and Athena Research Center. working within the research team ErgaLab under the supervision of professor Ioannis Z. Emiris. I am also a Marie Skłodowska-Curie fellow. My project is framed within the European network GRAPES. I am originally from Barcelona and I studied for my bachelor's degree in mathematics at the Faculty of Mathematics and Statistics of Universitat Politècnica de Catalunya and my master's double joint degree in Algebra, Geometry and Number Theory at the Universittà degli studi di Padova and Universiteit Leiden within the ALGANT program.
My interests are mainly in toric geometry and sparse or multihomogeneous polynomial systems. I investigate on resultants and Gröbner bases and their applications in implicitization and elimination theory. Moreover, I also study the relation of such practical objects with some invariants of commutative algebra like the Castelnuovo-Mumford regularity. I am also very interested in tropical geometry.
Contact
email: carlescheca3@gmail.com, ccheca@di.uoa.gr
Department of Informatics and Telecomunications. Zografou 161 22, Greece.
"It's not how I'm computing, it's what it is!"
Check here a presentation on why the regularity is so important for computations with polynomial systems.
Journal articles
Mixed Subdivisions Suitable for the Greedy Canny–Emiris Formula. with Ioannis Z. Emiris, Mathematics of Computer Science 18, 3 (2024). https://doi.org/10.1007/s11786-024-00577-y
Proceedings
A Greedy Approach to the Canny-Emiris Formula, ISSAC '22: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, with Ioannis Z. Emiris, Villenueve d'Asq, July 2022, pages 283–291, https://doi.org/10.1145/3476446.3536180.
Preprints
Toric Sylvester forms, with Laurent Busé, submitted.
In preparation
Multigraded Castelnuovo-Mumford regularity and Gröbner bases, with Matías Bender, Laurent Busé and Elias Tsigaridas
Upcoming events and presentations
Positive Solutions of Polynomial Systems Arising from Real-life Applications. Banff International Research Station. 19-24 of May 2024. Granada, Spain.
Encuentro de Álgebra Computacional y Aplicaciones. Universidad Complutense de Madrid. 24-26 of June 2024. San Lorenzo del Escorial, Spain.
MEGA 2024. Max Planck Institute for Mathematics in Science. 29-2 of July of 2024. Leipzig, Germany.
Organizing
AROMATH Group Seminar. 13th of February of 2023, Athens. List of abstracts.
SIAMAG23: Minisymposium called "Castelnuovo-Mumford regularity and applications" joint with Laurent Buse and Pablo González-Mazón, Eidhoveen, 10th to 14th of July.
Software
Resultant of n-zonotopes and multihomogeneous systems with type functions.
Currently collaborating with Bernard Mourrain Bernard Mourrain for a JULIA package on Algebraic Modelling AlgebraicSolvers.jl
Bachelor and Master Studies: FME-UPC (Barcelona), Universittà degli studi di Padova (Padova), Leiden Universiteit (Leiden), ALGANT. Bachelor's thesis and Master's thesis