Geometry, Algebra and their applications

Unirationality, Hilbert schemes, and singularities PRIN 2022 Principal Investigator: Giovanni Staglianò (Unict) Start date: February 2025 Team: Alessio Sammartano (local coordinator) Alessio D'Alì Andreas Hochenegger Paolo Lella Roberto Notari Enrico Schlesinger Paolo Sentinelli Keywords:

commutative algebra
algebras and rings
homological algebra
category theory
algebraic geometry
unirationality
Gröbner deformations

Differential-Geometric Aspects of manifolds via Global Analysis PRIN 2022 Principal Investigator: Giuseppe Pipoli (UNIAQ) Start date: September 2023 - End date: September 2025 Team: Giovanni Catino (local coordinator) Alberto Roncoroni External collaborators: Luciano Mari(UNIMI) Paolo Mastrolia(UNIMI) Marco Rigoli(UNIMI) Reto Buzano(UNITO) Luigi Vezzoni(UNITO) Giuseppe Pipoli(UNIAQ) Lucio Bedulli(UNIAQ) Mario Santilli(UNIAQ) Keywords:

geometry and global analysis
differential geometry
Eintstein equations
submanifolds
geometric flows
special structures

Squarefree Gröbner degenerations, special varieties and related topics PRIN 2020 Principal Investigator: Matteo Varbaro (Unige) Start date: January 2022 Team: Paolo Lella (local coordinator) Roberto Notari Alessio Sammartano Enrico Schlesinger Paolo Dulio Paolo Sentinelli Alessio D'Alì External collaborators: Matteo Varbaro (Unige) Aldo Conca (Unige) Marilina Rossi (Unige) Alessandro De Stefanis (Unige) Emanuela De Negri (Unige) Alessio Caminata (Unige) Francesco Russo (Unict) Marco D'Anna (Unict) Giovanni Staglianò (Unict) Elena Guardo (Unict) Giuseppe Zappalà (Unict) Carmelo Finocchiaro (Unict) Francesco Polizzi (Unical) Keywords:

commutative algebra
algebras and rings
homological algebra
category theory
algebraic geometry
combinatorics
Gröbner deformations

Canonical structures on manifolds GNSAGA 2024 Start date: March 2024 - End date: March 2025 Team: Alberto Roncoroni (PI) Giovanni Catino External collaborators: L. Branca (UNIMI) D. Dameno (UNIMI) P. Mastrolia (UNIMI) Keywords:

geometry and global analysis
differential geometry
Eintstein equations
submanifolds
geometric flows
special structures

New theoretical perspectives via Gröbner bases GNSAGA 2023 Start date: March 2023 - End date: March 2024 Team: Alessio D'Alì (PI) Alessio Sammartano External collaborators: A. Caminata (UNIGE) A. De Stefani (UNIGE) Keywords:

Gröbner bases
triangulation
Grassmannian
Betti numbers
determinantal ideal
cohomologically full monomial ideals
F-singularity
blowup algebra

Geometric and discrete tomography and applications Team: Paolo Dulio External collaborators: Paolo Finotelli (Polimi) Carla Peri (Unicatt) Silvia M.C. Pagani (Unicatt)

Superoscillations and spaces of holomorohic functions Team: Irene Sabadini Stefano Pinton External collaborators: Yakir Aharonov (Chapman University and Tel Aviv University) Fabrizio Colombo (Polimi) Shmuel Nussinov (Chapman University and Tel Aviv University) Daniele C. Struppa (Chapman University) Jeff Tollaksen (Chapman University)

Geometric methods for space-time signal processing Team: Roberto Notari External collaborators: Marco Compagnoni (Polimi) Fabio Antonacci (Polimi) Augusto Sarti (Polimi)

Research projects