Gabriele Vezzosi: Difference between revisions
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Revision as of 11:00, 11 February 2018
 | This article, Gabriele Vezzosi, has recently been created via the Articles for creation process. Please check to see if the reviewer has accidentally left this template after accepting the draft and take appropriate action as necessary.
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Comment: Needs references that are about him, not by him. The Drover's Wife (talk) 13:02, 9 February 2018 (UTC)
Gabriele Vezzosi is an italian mathematician, born in Florence (Italy). His main interest is Algebraic Geometry.
He has a MS degree in Physics (University of Florence, under the supervision of Alexandre M. Vinogradov) and a PhD in Mathematics (Scuola Normale Superiore, Pisa, under the supervision of Angelo Vistoli). His first papers dealt with differential calculus over commutative algebras, intersection theory, (equivariant) algebraic K-theory, motivic homotopy theory, and existence of vector bundles on singular algebraic surfaces.
Around 2001-2002 he started his collaboration with Bertrand Toën. Together, they created Homotopical Algebraic Geometry (HAG)[1][2] [3], whose more relevant part is Derived Algebraic Geometry (DAG) [4][5] which is by now a powerful and widespread theory [6]. Slightly later, this theory have been reconsidered, and highly expanded by Jacob Lurie.
More recently, Vezzosi together with Tony Pantev, Bertrand Toën and Michel Vaquié defined a derived version of symplectic structures[7] and studied important properties and examples (an important instance being Kai Behrend's symmetric obstruction theories); further together with Damien Calaque these authors introduced and studied a derived version of Poisson and coisotropic structures[8] with applications to deformation quantization [9].
Lately Toën and Vezzosi (partly in collaboration with Anthony Blanc and Marco Robalo) moved to applications of derived and non-commutative geometry to arithmetic geometry, especially to Spencer Bloch's conductor conjecture[10][11].
Vezzosi also defined a derived version of quadratic forms, and in collaboration with Benjamin Hennion and Mauro Porta, proved a very general formal gluing result along non-linear flags[12] with hints of application to a yet conjectural Geometric Langlands Program for varieties of dimension bigger than 1. Together with Benjamin Antieau, Vezzosi proved an HKR theorem for varieties of dimension p in characteristic p[13].
Vezzosi spent his career so far in Pisa, Florence, Bologna and Paris, has had 3 Phd students, so far (Schürg, Porta and Melani), and is currently full professor at the University of Florence (Italy).
References
- ^ Toen, Bertrand; Vezzosi, Gabriele (2005). "HAG I". Advances in Mathematics. 193 (2): 257–372.
- ^ Toen, Bertrand; Vezzosi, Gabriele (2008). "HAG II". Memoirs of the AMS. 193 (902): 1–228.
- ^ "ncatlab entry: Homotopical Algebraic Geometry". ncatlab. Retrieved February 10, 2018.
- ^ "Derived Algebraic Geometry". Wikipedia. Retrieved February 10, 2018.
- ^ "ncatlab entry: Derived Algebraic Geometry". ncatlab.
- ^ "Harvard DAG learning seminar". Retrieved February 10, 2018.
- ^ "Shifted symplectic structures". Publ. Math. IHES. 17 (1): 271–328. 2013. doi:10.1007/s10240-013-0054-1.
- ^ "Shifted Poisson structures and deformation quantization,". Journal of Topology. 10 (2): 483–584. 2017.
- ^ Toen, Bertrand. "Derived algebriac geometry and deformation quantization" (PDF). ICM-talk (2014). Retrieved February 10, 2018.
- ^ Blanc, A.; Robalo, M.; Toen, B.; Vezzosi, G. "Motivic Realizations of Singularity Categories and Vanishing Cycles". arXiv.
- ^ Toen, B.; Vezzosi, G. "Trace formula for dg-categories and Bloch's conductor conjecture I". arXiv.
- ^ Hennion, B.; Porta, M.; Vezzosi, G. "Formal gluing along non-linear flags". arXiv.
- ^ Antieau, B.; Vezzosi, G. "A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p". arXiv.
External links
- Personal web page
- Gabriele Vezzosi at the Mathematics Genealogy Project
- Gabriele Vezzosi Wikipedia entry in german
- Ncatlab entry on derived algebraic geometry
- Wikipedia entry on Derived Algebraic Geometry
Category:1968 births
Category:Living people
Category:Italian mathematicians
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