Hola! Hi! Χαίρετε! Ciao! Hej! I am Carles Checa and (since September 2024) I am a postdoc in the University of Copenhagen, under the supervision of Elisenda Feliu. Our work is funded by the ERC consolidator grant “Signs, polynomials, and reaction networks” (POSALG-101044561), with PI Elisenda Feliu.

I defended my PhD in the NKUA (supervised by Ioannis Emiris) on June 2024. 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 Università degli studi di Padova and Universiteit Leiden within the ALGANT program. See my CV.

My interests are mainly in sparse/multihomogeneous polynomial systems and algebraic elimination, i.e. the use of resultants and Gröbner bases. Thus, some of my current interests include:

• Parametrizing the positive solutions of polynomial systems that appear in applications, such as those appearing in the theory of chemical reaction networks. Also, deciding upon the multiple positive solutions of those systems.

• Providing effective criteria for birrationality of polynomial maps in the framework of geometric modelling.

• Upper and lower bounds to the number of positive solutions of fewnomial systems.

• Finding compact formulas for the computation of the sparse resultant.

• The relation between Gröbner bases, multigeneric initial ideals and the multigraded Castelnuovo-Mumford regularity. In particular, how to use the multigraded regularity to solve systems that are 0-dimensional (or have 0-dimensional projections).