Derived algebraic geometry serves as the primary focus for Gabriele Vezzosi, an Italian mathematician born in 1966. Having completed his education at the Scuola Normale Superiore, he transitioned into a career characterized by extensive collaborative research into the intersection of algebraic geometry and homotopical methods, fundamentally shaping the current development of modern mathematical theory.
Academic Foundations and Early Research
Vezzosi began his academic training at the University of Florence, where he secured a Master of Science degree in Physics under the guidance of Alexandre M. Vinogradov. He later completed his doctoral studies in mathematics at the Scuola Normale Superiore in Pisa, supervised by Angelo Vistoli. His early publications concentrated on differential calculus within commutative rings, intersection theory, motivic homotopy theory, and the presence of vector bundles on singular algebraic surfaces.
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Take the IQ test →The Development of Derived Algebraic Geometry
Starting in 2001 and 2002, a professional partnership with Bertrand Toën led to the creation of homotopical algebraic geometry. This framework, specifically derived algebraic geometry, has become a widely adopted methodology. Subsequent work expanded this field, including contributions from Jacob Lurie. Vezzosi has continued to refine these structural theories, exploring derived versions of symplectic, Poisson, and coisotropic structures alongside researchers like Tony Pantev and Michel Vaquié. These developments have provided new insights into symmetric obstruction theories and deformation quantization.
Recent Mathematical Contributions
In more recent years, his investigations have pivoted toward the intersection of derived and non-commutative geometry with arithmetic geometry. Working with collaborators such as Anthony Blanc and Marco Robalo, he has examined the conductor conjecture proposed by Spencer Bloch. Further projects include the formal gluing of non-linear flags with Mauro Porta and Benjamin Hennion, suggesting applications for the Geometric Langlands program. Additionally, he collaborated with Benjamin Antieau to establish a Hochschild–Kostant–Rosenberg theorem applicable to varieties of dimension p in characteristic p.
Career Appointments and Institutional Influence
Throughout his professional tenure, Vezzosi has held academic positions in Florence, Pisa, Bologna, and Paris. His institutional record includes a stint at Paris Descartes University during the 2014–2015 academic year, and he currently holds a professorship at the University of Florence. Beyond his research output, he served as an organizer for the 2015 Oberwolfach Seminar on Derived Geometry and the 2019 thematic program on derived algebraic geometry at the Mathematical Sciences Research Institute in Berkeley, California. He has supervised the doctoral studies of Schürg, Porta, and Melani.
Fast facts
- Born: 1966
- Nationality: Italian
- Primary Field: Algebraic Geometry
- PhD Institution: Scuola Normale Superiore
- Current Position: Full Professor at the University of Florence
- Notable Collaboration: Bertrand Toën
- Academic Supervision: Alexandre M. Vinogradov and Angelo Vistoli
Questions readers ask
What is homotopical algebraic geometry?
It is a field created by Gabriele Vezzosi and Bertrand Toën around 2001–2002, with derived algebraic geometry acting as its most significant component.
Where has Vezzosi taught?
He has held academic roles in Florence, Pisa, Bologna, and Paris, including a position at Paris Descartes University and his current professorship at the University of Florence.
Achievements
- Held posts at University of Florence and Paris Descartes University
