| 词条 | Gabriele Vezzosi |
| 释义 |
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 rings, 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] which is by now a powerful and widespread theory.[5][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][12] 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[13] 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 Hochschild-Kostant-Rosenberg theorem (HKR) for varieties of dimension p in characteristic p.[14] In 2015 he organised the Oberwolfach Seminar on Derived Geometry[15] at MFO-Oberwolfach (Germany), and is an organiser of the one semester thematic program at MSRI (Berkeley) in 2019 on Derived algebraic geometry.[6] Vezzosi spent his career so far in Pisa, Florence, Bologna and Paris, has had three PhD students (Schürg, Porta and Melani) and is full professor at the University of Florence (Italy). References1. ^{{cite journal |last1=Toen|first1=Bertrand |last2=Vezzosi|first2=Gabriele |title=HAG I|journal=Advances in Mathematics|date=2005|volume=193|issue=2|pages=257–372}} 2. ^{{cite journal|last1=Toen|first1=Bertrand|last2=Vezzosi|first2=Gabriele|title=HAG II|journal=Memoirs of the AMS|date=2008|volume=193|issue=902|pages=1–228}} 3. ^{{cite web|title=ncatlab entry: Homotopical Algebraic Geometry|url=https://ncatlab.org/nlab/show/homotopical+algebraic+geometry |website=ncatlab |accessdate=February 10, 2018}} 4. ^{{cite web|title=ncatlab entry: Derived Algebraic Geometry|url=https://ncatlab.org/nlab/show/derived+algebraic+geometry|website=ncatlab}} 5. ^{{cite web|title=Harvard DAG learning seminar|url=http://people.fas.harvard.edu/~amathew/dag.html |accessdate=February 10, 2018}} 6. ^1 {{cite web|last1=MSRI|title=Program "Derived Algebraic Geometry"|url=https://www.msri.org/programs/306|website=MSRI|accessdate=April 19, 2018}} 7. ^{{cite journal|title=Shifted symplectic structures|journal=Publ. Math. IHES|date=2013|volume=17|issue=1|pages=271–328|doi=10.1007/s10240-013-0054-1|arxiv=1111.3209}} 8. ^{{cite journal|title=Shifted Poisson structures and deformation quantization,|journal=Journal of Topology |date=2017 |volume=10|issue=2 |pages=483–584}} 9. ^{{cite web |last1=Toen |first1=Bertrand|title=Derived algebraic geometry and deformation quantization|url=https://perso.math.univ-toulouse.fr/btoen/files/2012/04/icm2014.pdf|website=ICM-talk (2014)|accessdate=February 10, 2018}} 10. ^{{cite arxiv |last1=Blanc|first1=A. |last2=Robalo|first2=M.|last3=Toen|first3=B. |last4=Vezzosi |first4=G.|title=Motivic Realizations of Singularity Categories and Vanishing Cycles|arxiv=1607.03012 }} 11. ^{{cite arxiv|last1=Toen|first1=B.|last2=Vezzosi |first2=G. |title=Trace formula for dg-categories and Bloch's conductor conjecture I|arxiv=1710.05902 }} 12. ^{{cite web|last1=Vezzosi|first1=Gabriele|title=Applications of non-commutative algebraic geometry to arithmetic geometry|url=https://www.youtube.com/watch?v=JCu_-Hab-DA|website=IHES channel- YouTube|accessdate=April 18, 2018}} 13. ^{{cite arxiv |last1=Hennion |first1=B.|last2=Porta| first2=M.|last3=Vezzosi|first3=G.|title=Formal gluing along non-linear flags |arxiv=1607.04503}} 14. ^{{cite arxiv|last1=Antieau|first1=B.|last2=Vezzosi|first2=G.|title=A remark on the Hochschild-Kostant-Rosenberg theorem in characteristic p|arxiv=1710.06039}} 15. ^{{cite web|last1=MFO Seminar |title=MFO Seminar, Derived Geometry|url=https://www.mfo.de/occasion/1548a |website=MFO |accessdate=April 18, 2018}} External links
3 : 1968 births|Living people|Italian mathematicians |
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