Alessandro Oneto

at BGSMath - UPC
Research area: Algebra / Mathematical Modelling

PhD in Mathematics obtained at Stockholm University (2016)

Biosketch

Since January 2018, I am a BGSMath Postdoc at UPC in the group of Marta Casanellas to work on problems in Algebraic Statistics. In particular, to study algebraic methods for statistical models related to Phylogenetics and Restricted Boltzmann Machines. 

From November 2016 to December 2017, I have been a Postdoc at Inria Sophia Antipolis Méditerranée (France) in the group of Bernard Mourrain to study algebraic algorithms for additive symmetric tensor decomposition.

In June 2016, I obtained my PhD degree in Mathematics at Stockholm University (Sweden) under the supervision of Boris Shapiro and Ralf Fröberg. Part of the arguments included in the final thesis have been developed in Spring 2015 during a long stay at Monash Univesity in Melbourne (Australia) under the mentoring of Enrico Carlini.

I did my undergraduate studies in Mathematics at Università degli Studi di Genova (Italy).

Research lines

My research interests are in applications of algebraic and geometric tools to problems related to tensor decompositions. These involve the study of Hilbert functions of 0-dimensional schemes and fat points, secant varieties of classical projective varieties as Veronese, Segre and Segre-Veronese varieties, apolarity theory and inverse systems. 

Selected publications

  1. "On the Hilbert function of general fat points in P1 x P1" with E. Carlini, and M.V. Catalisano. [ArXiv pre-print]

  2. "Minkowski sums and Hadamard products of algebraic varieties" with N. Friedenberg and R. Williams. Combinatorial Algebraic Geometry: Selected papers from the 2016 Apprenticeship Program (eds. G.G. Smith and B. Sturmfels), AMS Series: Fields Institute Communications (2017)[ArXiv pre-print]  [Book chapter]

  3. "Waring loci and Strassen conjecture" with E. Carlini and M.V. Catalisano. Advances in Mathematics 314, pgg.: 630--662 (2017) [ArXiv pre-print] [Journal]
  4. "On the real rank of monomials" with E. Carlini, M. Kummer and E. Ventura. Mathematische Zeitschrift 286(1), pgg.: 571--577 (2017) [ArXiv pre-print] [Journal]

  5. "Waring-like decompositions of polynomials - 1" with M.V. Catalisano, L. Chiantini and A.V. Geramita. Linear Algebra and its Applications 533, pgg.: 311-325 (2017)[ArXiv pre-print] [Journal]