Roser Homs Pons
My main research interests are in commutative algebra and its computational aspects. In my thesis I addressed the problem of approximating local rings by Gorenstein rings in the zero-dimensional case, under the supervision of Joan Elias. In particular, I studied how far is a local k-algebra from being Gorenstein and which are its minimal Gorenstein covers, that is, those Gorenstein rings that are at minimal distance. We mainly approach this problem from the perspective of Macaulay's inverse systems.
Primary ideals and their differential equations, with Yairon Cid-Ruiz and Bernd Sturmfels, arXiv:2001.04700.
Computing minimal Gorenstein covers, with Juan Elias and Bernard Mourrain, to appear in J. Pure Appl. Algebra 224 (2020), arXiv:1901.04165.
On low Gorenstein colength, with Juan Elias, J. Algebra 513 (2018), 368-387.
On the analytic type of Artin algebras, with Juan Elias, Comm. Algebra 44.6 (2016), 2277-2304.
Canonical Hilbert-Burch matrices in k[[x,y]], with Anna-Lena Winz.
I obtained my PhD on July 2019 at Universitat de Barcelona under the supervision of Joan Elias. From August to December 2019, I stayed at TU Berlin for a short-term postdoc in the frame of the Thematic Einstein Semester on Algebraic Geometry under the supervision of Michael Joswig and Bernd Sturmfels. Since the start of 2020, I am a postdoc at the Max-Planck-Institut in Leipzig in the Nonlinear Algebra research group of Bernd Sturmfels.