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Scicli, Sicily

Giuseppe Favacchio

Short Bio. I was born on 7th of January 1985 in Scicli, Italy. I graduated (2011) and obtained the PhD in Mathematics (2014) at the Università degli Studi di Catania (Italy) under the supervision of Alfio Ragusa. From August 2012 to February 2013 I was a visiting student of Juan Migliore at University of Notre Dame, South Bend (IN). In 2015 I obtained the Italian qualification for teaching Mathematics and Physics in High Schools (TFA classe A049). I have been a postdoctoral researcher at Università degli studi di Catania from August 2016 to August 2020, advisor Elena Guardo (prev. Alfio Ragusa). During this time I taught "Algebraic methods in Code Theory and Cryptography" to graduate students (2016) and "Linear Algebra and Geometry" to undergraduate students (from 2017 to 2020). I visited Juan Migliore at University of Notre Dame (in 2017, 2018 and 2019), Adam Van Tuyl at McMaster University in Hamilton (ON) Canada (Jan 2019) and Enrico Carlini at Politecnico di Torino (TO) Italy (Oct 2019). I have been a postdoctoral researcher at Politecnico di Torino, advisor E Carlini, from Oct 2020 to Dec 2021.

Since January 2022 I'm a Senior Researcher (RTDb) at Università degli Studi di Palermo.

My profile on GoogleScholar, Scopus, ResearchGate .

Research Interests: Interaction between Commutative Algebra, Algebraic Geometry and Combinatorics. With a focus on

Schemes with an unexpected behavior under a general projection and their potential applications to "contextuality" in Quantum Mechanics. This includes configurations of points whose GEneral PROjection is a Complete Intersection (geproci sets);
Unexpected Hypersurfaces and vanishing conditions on linear systems;
Varieties supported by algebraic structures, such as Hadamard products and varieties of tensors;
Algebraic and homological invariants of low dimensional schemes in multiprojective spaces. This includes the description of ACM property, Hilbert function, resolution of schemes of points or lines in a multiprojective space;
Hilbert function and Betti numbers of multigraded algebras;
Algebraic and homological properties of Toric ideals of graphs;
Configurations of points with some connection to design theory. Star configurations. Steiner configurations;
Associated primes of powers of squarefree monomial ideals;
Weak Lefschetz Property.