Pablo González-Mazón

I am a Postdoctoral researcher at the Università di Trento, working within the Analytic and Algebraic Geometry and TensorDec teams, under the supervision of Professor Elisa Postinghel. I am also a fellow at the Italian Network for Applied and Birational Algebraic Geometry (INABAG). Before, I was a Ph.D. student at the Centre Inria d'Université Côte d'Azur working within the research team AROMATH, under the supervision of Professor Laurent Busé. I was a Marie Skłodowska-Curie fellow, and my project was framed within the European network GRAPES. As an undergraduate, I studied for two bachelor's degrees in mathematics and physics at the Universidad de Cantabria. Additionally, I studied an M2 in mathematics at the Université Gustave Eiffel as a Labex Bézout fellow.

Topics of interest:

My research focuses on the study of birational transformations defined over multiprojective spaces, and the use of polynomials to extract information for data.  

Birational maps pose multiple challenges, and have historically occupied a central role in algebraic geometry. However, much of the classic literature has primarily concentrated on birational automorphisms of projective spaces - also known as Cremona maps - rather than giving equal attention to birational maps between multiprojective spaces. The study of multiprojective spaces is a very active topic in commutative algebra, driven by multiple theoretical inquiries and its real-world applications due to the connection with tensor product maps. Additionally, during the last decade interest in birational transformations within geometric modeling and computer-aided geometric design (CAGD) has surged, and several works dedicated to their construction and manipulation have appeared.

In the example, a teapot is enclosed in a parallel-faced box of similar dimensions. A user can decide new positions for the vertices of the box, giving place to a “rational deformation of the box” and of the teapot. 

In my research, I develop tools for the effective construction of such transformations, with the special property that there is an ''inverse rational transformation'', i.e. they are birational. Of course, this problem requires the study of algebro-geometric properties of birational maps and relies on tools from algebraic geometry and commutative algebra. Not surprisingly, if the rational map is defined by multilinear polynomials tensors come into play.