GABRIELE VEZZOSI’s CURRICULUM VITÆ
EDUCATION and POSITIONS
- October 10, 1994 - degree in Physics (110/110 cum laude) Università di Firenze, title
of Thesis “Algebraic Geometry of PDE’s and a point of view on quantization” , advisor
Prof. Alexandre M. Vinogradov (Moscow);
- December 1995 - December 1998: PhD Program in Mathematics at Scuola Normale
Superiore (Pisa, Italy);
- May 13, 1999 - PhD Thesis’ defense (70/70 cum laude) “The Chow ring of the classifying
stack of PGL3” at Scuola Normale Superiore (Pisa, Italy) (Advisor: Prof. A. Vistoli
(Bologna); Jury: Prof. E. Arbarello (SNS, Pisa), Dr. B. Totaro (Cambridge), Prof. G.
Tomassini (SNS, Pisa), Dr. M. Manetti (SNS, Pisa));
- March 1999-December 2003: PostDoc position at Dipartimento di Matematica, Università
di Bologna, on the Project “Intersection Theory”;
- 26 February 2001, Qualification asMaitre de Conferences (Section 25 -Mathematiques)
by Minist`ere de l’Education Nationale (France);
- February 2003, winner of an Assistant Professor (Ricercatore) position in Geometry
(MAT-03), Facolt`a di Ingegneria, Universit`a di Firenze;
- January 2004 - 29 December 2010, Assistant Professor (Ricercatore) in Geometry
(MAT-03) at Dipartimento di Matematica Applicata “G. Sansone”, Facoltà di Ingegneria
dell’Universit`a di Firenze.
- February 2006, winner of a Concorso (Job Competition in English, Concours in
french) as Full Professor (PR1) in Geometry - National Job Competition held at the University
of Bologna - Italy.
-March 2009, Qualification `a Professeur byMinist`ere de l’Education Nationale (France).
- October 2010, shortlisted for a Full Professor position in Geometry at ETH, Z¨urich
(Switzerland).
- 30 December 2010 - present, permanent Full Professor position in Geometry at Università
di Firenze (Italy). On leave since January 2013- July 2014.
- May 15, 2012, qualified first in Concours `a Professeur, Université Paris Diderot - Paris 7,
Paris, France
- January 2013 - July 2014 (resigned), Professeur at Institut de Mathématiques de
Jussieu, Université Paris Diderot - Paris 7, Paris, France.
- July 2014- present, Full Professor of Geometry, Dipartimento di Matematica ed Informatica
“ Ulisse Dini” Università di Firenze (Italy).
VISITS and POSITIONS ABROAD
- 1997, Spring Semester: visiting fellow all’Harvard Department of Mathematics (Cambridge,
Boston, Mass., USA);
- February 10 - March 1, 1999: Visiting Fellow at Department of Mathematics and
Mathematical Statistics, Cambridge University, Cambridge UK (collaboration with Prof.
Burt Totaro);
- March 1 - March 31, 2000: visitor at the Institute for Advanced Study, Princeton
NJ, USA (“Motivic Homotopy Theory Program” org. V. Voevodsky);
- November, 2000: visitor at Max Planck Institut f¨ur Mathematik, Bonn, Germany;
- February-March 2001, visitor at the Department of Mathematics, University of Utah,
Salt Lake City (USA);
- April 2001, Maitre de Conferences invit´e (1 month) at the Institut Fourier, Grenoble,
France;
- June 2001, Maitre de Conferences invit´e (1 month) at Department de Mathematique,
Laboratoire J. Dieudonn´e Universit´e de Nice (France);
- March-April 2002, member of the MSRI (Mathematical Sciences Research Institute)
Berkeley, CA - USA;
- October 6-24, 2002, Research in Pairs Program at Mathematisches Forschungsinstitut
Oberwolfach, Germany (with B. Toen, Title From homotopical algebraic geometry to
derived algebraic geometry);
- June 2003, visitor alla FachbereichMathematik und Informatik,Westf¨alischeWilhelms-
Universit¨at M¨unster, M¨unster (Germania).
- May 16-26, 2004, visitor presso il Matematisk Institutt, Univ. Oslo (Norway).
- July 3-20, 2004, visitor presso il CIRGET (Centre Interuniversitaire des Recherches
en Géométrie et Topologie), Université du Quebèc à Montreal (Montreal, Canada).
- Fall 2006, visitor at Matematisk Institutt, Univ. Oslo (Norway).
- February 2007, Special Program in Algebraic Geometry, Institute for Advanced Study,
Princeton, USA.
- April 2007, Ohio State University, Columbus, Ohio, USA.
- May 13-20, 2007 - Workshop Stacks in geometry and topology, Fields Institute,
Toronto, Canada.
- September 2007 - visitor SISSA, Trieste. Italy.
- March 2008 - Special Program in Representation theory, algebraic geometry and
physics, Institute for Advanced Study, Princeton, USA.
- May 2008, Professeur invité, Institut de Mathématiques, Universit´e Paul Sabatier,
Toulouse, France.
- May 2009, invited professor at Mathematisches Institut der Universit¨at Bonn.
- November 2010, visitor at I3M, Universit´e de Montpellier2, Montpellier, France.
- March-May 2012, visitor at Institut des Hautes Etudes Scientifiques (IHES), Bures Sur-
Yvette, Paris, France.
- April 30 - May 4, 2012, visitor at at I3M, Université de Montpellier2, Montpellier,
France.
- September 8- September 13, 2013, visitor at Galileo Galilei Institute for Theoretical
Physics, Arcetri (Florence), Italy.
- April 13-19, 2014, visitor at at I3M, Université de Montpellier2, Montpellier, France.
- June 2-6, 2014, visitor at the Oxford Mathematical Institute, Oxford, UK.
- March 1- March 31, 2015, Visiting Member at Institute for Advanced Study, Princeton,
USA.
- May 1- May 31, 2015, Visiting Member at Institut des Hautes Etudes Scientifiques
(IHES), Bures-sur-Yvette, Paris, France.
- May 1-May 31, 2016, Professeur invité, Institut de Mathématiques de Jussieu-Paris
Rive Gauche, Paris, France.
- October-December, 2018, Professeur invité, Institut de Mathématiques, Université
Paul Sabatier, Toulouse, France.
- January 22 - May 24, 2019, member of the MSRI (Berkeley) as an Organizer of the
Program Derived Algebraic Geometry.
- January 29-February 8, 2020, visitor at IRMA Strasbourg (France).
- March 2021, visitor IMT, Toulouse (France).
- April 2022, visitor IMT, Toulouse (France).
INVITED TALKS
- October 3-8, 1994: invited talk “On higher de Rham complexes” all’ “International
Conference on Secondary Differential Calculus and Nonlinear Problems in Physics”, Vietri
sul Mare, Italy;
- 29 August- 4 September 1999: Conference “Proprietà geometriche delle variet`a reali
e complesse: nuovi contributi Italiani ”, Mondello (Palermo), invited talk “The Chow ring
of the classifying stack of PGL(3)”;
- March 26-28 1999: invited talk “The Chow ring of the classifying stack of PGL3” at
the Conference “Algebraic cycles: Hodge theory, Motives and K -theory”, Dipartimento
di Matematica dell’Università di Genova (organized by L. Barbieri-Viale, C. Pedrini, V.
Srinivas);
- December 1999, International Conference on Intersection Theory (Bologna), invited
talk “On the Chow ring of the classifying space of PGL3”;
- April 1- April 5 2000, invited talk at University of Missouri at Columbia (MO-USA),
“Classifying spaces in Algebraic Geometry”;
- June 22-23, 2000: 2 invited talks “Introduction to A1-homotopy theory”, “Some open
problems in A1-homotopy theory”, Dipartimento di Matematica dell’Università di Genova
(organized by Prof. C. Pedrini);
- 28 February 2001, talk “Motivic refined cycle maps”, Department of Mathematics,
University of Utah, Salt Lake City (USA);
- April 6, 20, 27, 2001, Grenoble, Institut Fourier, invited talks “Some open problems in
A1-homotopy theory”, “Higher equivariant algebraic K-theory of group actions with finite
stabilizers” and “Higher algebraic equivariant K-theory for diagonalizable group schemes”;
- June 14, 21, 2001, Nice, Laboratoire J. A. Dieudonn´e: invited talk “Higher algebraic
equivariant K-theory for diagonalizable group schemes” at the Workshop “Rencontres
Nice-Genes” and talk “Algebraic Geometry over model categories: a general approach to
derived algebraic geometry” at Séminaires de Géométrie ;
- 21-25, November 2001 - Laboratoire J. Dieudonné, Nice (Francia), Workshop “CATS
1: Higher Categorical Structures in Algebraic Geometry ”, talk “Algebraic Geometry over
model categories”;
- March 2002, invited speaker at the Workshop “Non-abelian Hodge Theory”, MSRI
(Berkeley, CA -USA); title of talk “Homotopy Algebraic Geometry”; Notes and Streaming
Video are available at:
http://www.msri.org/publications/ln/msri/2002/hodgetheory/vezzosi/1/index.html);
- June 2002, invited speaker at “WAGP2002-Workshop on Algebraic Geometry and
Physics- K-Theory, Derived Categories and Strings”, Dipartimento di Matematica, Università
di Genova (25-28 June 2002); title of talk “Homotopy Algebraic Geometry”;
- August 4 - 10, 2002, Mathematisches Forschungsinstitut Oberwolfach, Algebraische
K-Theorie (org. Dan Grayson (Urbana), Uwe Jannsen (Regensburg), Bruno Kahn
(Paris)), invited speaker;
- October 25-26, 2002, Universitat Essen, DFG SCHWERPUNKT-Globale Methoden
in der Komplexen Geometrie- Workshop “From homotopical algebra to homotopical
algebraic geometry”, Speakers: Bertrand Toen and Gabriele Vezzosi (Organizzato da
H´el`ene Esnault, Stefan M¨uller-Stach, Eckart Viehweg). Informations and nots available
at: http://www.uni-essen.de/˜mat930/homotopy.html.
- December 2002, Isaac Newton Institute for Mathematical Sciences (Cambridge, UK),
Euroworkshop Elliptic Cohomology and Higher Chromatic Phenomena (9 - 20 December
2002), invited talk “An idea of homotopical algebraic geometry” (Dec. 20, h. 15:30).
Notes are available at
http://www.newton.cam.ac.uk/webseminars/pg+ws/NSTW04/201202/vezzosi/ ;
- 17-25, May 2003 - Laboratoire J. Dieudonn´e, Nice (Francia), Workshop “CATS
2: Higher Categorical Structures in Algebraic Geometry ”; title of talk “Derived moduli
spaces”;
- 16 June 2003, Fachbereich Mathematik und Informatik, Westf¨alische Wilhelms-
Universit¨at M¨unster, M¨unster (Germania), talk “K-theory depends only on the simplicial
localization”.
- 8-13 September 2003, invited speaker at Congresso dell’Unione matematica Italiana
(Milano - Università Milano Bicocca).
- 18-20 December 2003, Meeting on Algebraic Varieties (Incontro di met`a periodo del
progetto MIUR - Geometria delle Variet`a Algebriche), Roma; title of talk “Homotopical
algebraic geometry and global derived moduli spaces”.
- March, 14-20, 2004, invited speaker at the workshop Motives and homotopy theory
of schemes, organized by T. Geisser (Los Angeles), B. Kahn (Paris), F. Morel (Paris),
Mathematisches Forschunginstitut Oberwolfach - Germany.
- March, 8-9 April, 2004, Dept. de Math., Universit´e de Geneve, talk “Homotopical
algebraic geometry: introduction and new directions”.
- May, 21, 2004, Colloquium (Felleskollokvium) talk “Algebraic Geometry on homotopy
theories” al Matematisk Institutt, Univ. Oslo (Norway).
- May 31 - June 6, 2004, Workshop “Derived non-abelian Hodge theory”, Toulouse
(France).
- June 11-18, 2004, invited speaker at “2004 Summer Program: n-Categories: Foundations
and Applications” (June 7-18, 2004, IMA Minneapolis, USA).
- August 19-28, 2005 Conference “The Arithmetic of Structured Ring Spectra”, Barony
Rosendal, Rosendal - Norway.
-May 2006,Workshop Derived Algebraic Geometry and Nonabelian Hodge Theory,Dept.
de Math., Nice - France.
- September 4-8, 2006, Topological Algebraic Geometry Workshop, Matematisk Institutt,
Oslo, Norway.
- November 2006, talk A derived moduli-theoretic approach to elliptic cohomology,
Labo. Picard, Univ. P. Sabatier, Toulouse, France.
- February 2007, Special Program in Algebraic Geometry, Institute for Advanced Study,
Princeton, USA.
- May 13-20, 2007, invited speaker Workshop "Stacks in geometry and topology",
Fields Institute, Toronto, Canada.
- 4-8 June 2007, invited speaker al convegno CIRM Algebraic Geometry in Higher Dimensions,
Levico Terme, Italy.
- June 2007, invited speaker at joint meeting UMI-DMF, Perugia, talk “An idea of
derived algebraic geometry”.
- March 2008, invited speaker Special Program in Representation Theory, Institute for
Advanced Study, Princeton, USA.
- 15-28 June 2008, invited speaker at the conference “Aspects of Moduli”, Centro de
Giorgi, Scuola Normale Superiore, Pisa, Italy.
- June 2008, invited speaker “HOCAT 2008. Homotopy Structures in Geometry and
Algebra. Derived Categories, Higher Categories”, Centre de Recerca Matematica, Bellaterra,
Barcelona, Spain.
- May 2009, invited talk Mathematisches Institut der Universit¨at Bonn, Germany.
- May 2009, invited talk Max Plank Institut f¨ur Mathematik, Bonn, Germany.
- 1-5 June, 2009, invited series of talks on Derived Algebraic Geometry (i-MATH
School on Derived Algebraic Geometry), Instituto Universitario de Fisica Fundamental y
Matem`aticas, IUFFyM, Salamanca, Spain.
- July 12 - August 02, 2009, “Dacha Seminar” on Recent Developments in Derived
Algebraic Geometry (Speakers: B. Toen, G. Vezzosi), Steklov Institute, Moscow, Russia.
- September 7-12, 2009, invited speaker at “Advanced School on Homotopy Theory
and Algebraic Geometry”, Mathematical Research Institute, University of Sevilla (IMUS),
Sevilla, Spain.
- April 19-22, 2010, invited speaker at the “Seminario di Geometria Algebrica” - Roma
La Sapienza- Rome, Italy.
- April 24 - May 7, 2010, invited speaker at Conference “Geometry at Large”, Fakult¨at
f¨ur Mathematik, Universit¨at Wien, Wien - Austria.
- May 24-30, 2010, invited speaker at GAD I - “Géométrie Algébrique à la Dérive” -
Montpellier, France (premi`ere rencontre autour du projet blanc ANR HODAG).
- August 29 - September 3, 2010, invited speaker at the Conference “Categorical methods
in geometry and gauge theory”, Chern Institute of Mathematics, Nankai University,
Tianjin - China.
- October 6, 2010, invited Colloquium talk & Job Interview (shortlisted for Professor
position), ETH-Zurich, Switzerland
- November 17, 2010, invited talk at Scuola Normale Superiore, Pisa, Italy.
- January 17-20, 2011, 2 invited talks on “Introduction to derived algebraic geometry
and applications”, Dipartimento di Matematica Pura e applicata, Università di Padova.
- March 28 - April 1, 2011, invited speaker at the International Conference on Homotopy
and Non-Commutative Geometry, Tbilisi State University, Tbilisi (Georgia).
- March 26, 2012, invited talk Derived algebraic geometry and obstruction theories,
with applications to stable maps to a K3 surface, Séminaire Analyse Algébrique, Institut
de Mathématiques de Jussieu, Paris 6, Paris - France.
-March 27, 2012, invited talk Derived symplectic structures and quantization , Séminaire
de Topologie, Université Paris Diderot, Paris 7, Paris - France.
- April 23, 2012, invited talk Derived symplectic structures and quantization , Séminaire
de G´eom´etrie, Institut Fourier, Grenoble - France.
- May 10, 2012, invited talk Derived symplectic structures and quantization, Séminaire
de Topologie Algébrique, LAGA - Institut Galilée, Paris 13, Paris - France
- May 3, 2013, invited talk First steps in derived symplectic geometry, Scuola Normale
Superiore, Pisa, Italy.
- May 10, 2013, invited talk First steps in derived symplectic geometry, ETHZ Moduli
Seminar, ETH, Z¨urich, Switzerland.
- May 30, 2013, invited talk First steps in derived symplectic geometry, Séminaire de
géométrie algébrique, Institut de Mathématiques de Jussieu, Paris, France.
- September 9, 2013, invited talk Derived symplectic geometry, Conference ’Geometry
of Strings and Fields’, Galileo Galilei Institute for Theoretical Physics, Arcetri (Florence),
Italy.
- October 9, 2013, invited talk at Réga (Reseaux Etudiants en Géométrie Algébrique),
Amphiteatre Darboux, IHP, Paris.
- January 24, 2014, invited talk at Séminaire Caen Cergy Clermont Paris - Th´eorie des
Repr´esentations, An overview of derived geometry, Bˆatiment Sophie Germain, Université
Paris Diderot, Paris.
- April 17, 2014, invited talk Université de Montpellier 2, First steps in derived logarithmic
geometry.
- March 2015, invited speaker at Conference Chow groups, motives and derived categories,
in Special Program ’Topology of algebraic varieties’, Institute for Advanced Study,
Princeton, USA.
- April 7-17, 2015, invited speaker at EPSRC Symposium Symplectic Techniques in
Derived Algebraic Geometry, Mathematics Institute, Warwick (UK).
- July 6-10, 2015, invited speaker at GAP (Geometry and Physics) XIII, IBS Center
for Geometry and Physics, Pohang, South Korea.
- July 20-25, 2015, invited speaker at Algebraic Geometry 2015, AMS Summer Institute
in Algebraic Geometry, University of Utah, Salt Lake City (US).
- March 06-16, 2016, invited at Program on Higher Structures in Geometry and Physics,
MPIm, Bonn (Germany).
- April 3-7, 2017, invited speaker at the Conference on invertible objects and duality in
derived algebraic geometry and homotopy theory, Regensburg, Germany. This Conference
is part of the Program “Higher Invariants” by SFB 1085 - Interactions between Arithmetic
Geometry and Global analysis.
- June 6-9, 2017, invited speaker at the Conference Algebraic Analysis in honor of
Masaki Kashiwara’s 70th Birthday, IHES, Paris, France.
- June 26-30, 2017, invited speaker at the Workshop Non-Archimedean geometry, motives
and vanishing cycles, Institut Mittag-Le✏er, Stockholm, Sweden.
- March 20-22, 2018, Kavli IPMU (Tokyo), invited speaker at the Workshop Lectures
on higher structures and quantisation (two talks, 1:30 h each).
- July 4-6, 2018, The Arithmetic of Derived Categories, CIRM, Trento (Italy).
- March 29, 2019, invited speaker at the workshop “Derived algebraic geometry and its
applications”, MSRI, Berkeley, USA; talk title Vanishing cycles, Bloch’s conductor conjecture
and non-commutative geometry.
- April 5, 2019, DAG Seminar, MSRI, Berkeley USA; talk title Formal gluing along
non-linear flags.
- November 27, 2019, Seminario di Geometria Algebrica ed Aritmetica (Università di
Pisa); talk title Decomposition along a non-linear flag.
- June 20-24, 2022, Toulouse, France: CATS-60 conference, to celebrate Carlos Simpson's 60th birthday;
talk title "An analog of Beilinson-Drinfeld Grassmannian for surfaces".
- 12 sep 2022 - 16 sep 2022, Antwerp (Belgium), Noncommutative Shapes: A conference in honour
of Michel Van den Bergh; talk title "An analog of Beilinson-Drinfeld Grassmannian for surfaces".
- 25 April 2023 - 28 sep 2023, Simons Center (Stony Brook, NY), Concluding Conference of Simons
Collaboration on Homological Mirror Symmetry, talk title "An analog of Beilinson-Drinfeld Grassmannian for surfaces".
-16-20 October, 2023, Categories and stacks in algebraic geometry and algebraic topology CATS 7 (Bertand Toën’s 50th birthday),
CIRM (Luminy), talk title "Integrability of foliations in positive characteristic".
- 10 May 2024, University of Rome (Tor Vergata), Algebra & Representation Theory Seminar (ARTS) joint session with Topology Seminar
"Analogs of Beilinson-Drinfeld's Grassmannian on a surface"
(this talk was part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006))
-May 27th, 2025, IMT Toulouse, Séminaire d'Homotopie et Géométrie Algébrique,
Gabriele Vezzosi, "Two dimensional versions of the affine Grassmannian"
SERIES OF LECTURES
- 1995: 5 lectures on “Groupoids in symplectic Geometry” at Dipartimento di Fisica
dell’Università di Firenze (Notes of the talks are available as Preprint DFF 225/04/1995
by the Dipartimento di Fisica);
- February-March 1998: 2 lectures, “Holonomy groupoids of a foliation and associated
C⇤-algebras”, “Spectra of abelian categories and Gabriel-Rosenberg reconstruction theorems
for general schemes”, in the Program “Introduction to Non-Commutative Geometry”,
Scuola Normale Superiore, Pisa (organized by Prof. G. Tomassini, SNS, Pisa) - Italy;
- November 1999, Dipartimento di Matematica, Università di Trento, series of lectures
on “Equivariant Intersection Theory”.
- October 2002, Univeritat Essen, DFG SCHWERPUNKT-Globale Methoden in der
Komplexen Geometrie - Workshop/School “From homotopical algebra to homotopical algebraic
geometry”, Speakers: Bertrand To¨en and Gabriele Vezzosi (Organizzato da Hélène
Esnault, Stefan M¨uller-Stach, Eckart Viehweg).
- September 2007 - Series of lectures “Derived Algebraic Geometry: Introduction and
open problems”, SISSA, Trieste - Italy.
- 1-5 June, 2009, invited series of talks on Derived Algebraic Geometry (i-MATH
School on Derived Algebraic Geometry), Instituto Universitario de Fisica Fundamental y
Matematicas, IUFFyM, Salamanca, Spain.
- July 12 - August 02, 2009, Dacha Seminar on Recent Developments in Derived Algebraic
Geometry (Speakers: B. Toen, G. Vezzosi), Steklov Institute, Moscow, Russia.
- September 7-12, 2009, invited series of lectures at ”Advanced School on Homotopy
Theory and Algebraic Geometry”, Mathematical Research Institute, University of Sevilla
(IMUS), Sevilla, Spain.
- January 10-16, 2010, invited speaker at the MFO-Oberwolfach Workshop Moduli
spaces in Algebraic Geometry, org. Dan Abramovich (Providence), Gavril Farkas (Berlin),
Stefan Kebekus (Freiburg).
- January - April 2011, Phd Course ’DG-categories and derived algebraic geometry’
(University of Padova, Italy).
- January 2013- June 2013, Séminaire Autour de la Géométrie Algébrique Dérivée,
organizer, run by my students, IMJ, Université Paris Diderot, Paris (webpage with Notes
http://www.math.jussieu.fr/⇠vezzosi/seminar/)
- September 2013- June 2014, Groupe de Travail Factorization algebras and derived
symplectic geometry, in collaboration with G. Ginot, V. Melani, M. Porta, IMJ, Paris.
- January 2014- July 2014, Séminaire Algèbre et topologie homotopiques, joint with G.
Maltsiniotis and B. Keller, IMJ, Paris.
- September 14-18, 2015, Summer School on Derived Algebraic Geometry, Collegio
Cairoli, Pavia (Italy).
- 22 Nov - 28 Nov 2015, Oberwolfach Seminar: Derived Geometry, MFO Oberwolfach
(Germany).
- 12-15, June 2017, ´Etat de la Recherche - DAGIT (Derived Algebraic Geometry and
Interactions), IMT Toulouse.
CONFERENCES AS AN ORGANIZER AND SCIENTIFIC COMMITTEE
MEMBER
- February 2002, with M.Manaresi (Bologna), C. Pedrini (Genova), A. Vistoli (Bologna),
organizer of the Workshop “K-Theory and Algebraic Cycles”, Bologna 7-9, February 2002
- Italy;
- 2007, May 30 - June 2, organizer with G. Ottaviani (Firenze) of the International
Workshop “Interactions with Algebraic Geometry” Firenze, May 30 - June 2, 2007 (supported
by Gruppo Nazionale Strutture Algebriche Geometriche ed Applicazioni, MIUR -
PRIN 2006 - Geometria delle variet`a algebriche e dei loro spazi di moduli, and Ente Cassa
di Risparmio di Firenze);
- September 2008, organizer with B. To¨en (CNRS, Toulouse), C. Simpson (CNRS,
Nice), T. Pantev (UPenn) of the Conference “CATS3 - Higher categories and Algebraic
Geometry”, Centro De Giorgi, Scuola Normale Superiore, Pisa - Italy. This was the third
conference of the CATS-series; the previous editions took place in Nice (2001 and 2003).
Among the participants to the whole series, so far: A. Bondal, K. Costello, V. Hinich,
A. Joyal, D. Kaledin, M. Kapranov, B. Keller, M. Kontsevich, J. Lurie, M. Olsson, T.
Pantev, J. Pridham, P. Schapira, V. Schechtman, Y. Soibelman, A. Yekutieli.
- July 2012, organizer with B. Toën (CNRS, Toulouse), C. Simpson (CNRS, Nice),
T. Pantev (UPenn), M. Vaqui´e (CNRS, Toulouse) of the Conference “CATS4 - Higher
categories and Algebraic Geometry”, 2-7 July 2012, CIRM - Luminy - France.
- 20-21 June, 2013, organiser with J-Y. Charbonnel, G. Danila, S. Morier-Genoud of
“Solstice 2013, G´eom´etries”, Institut de Math´ematiques de Jussieu, Paris, France. List
of Speakers : A. Corti (Imperial College London, England), V. Kac (M.I.T, USA), D.
Kaledin ( Russian Academy of Sciences, Moscow ), A. Kirillov (University of Pennsylvania),
M. Kontsevich (I.H.E.S), V. Ovsienko (Universit´e Claude Bernard Lyon 1, France),
R. Pandharipande (ETH-Zurich, Switzerland), J. Souto (University of Vancouver), B.
Thibert (Universit´e de Grenoble), B. To¨en (Universit´e de Montpellier).
- December 9th - 11th, 2013, organizer with L. Katzarkov (Univ. of Miami and Wien
Univ.) and B. To¨en (CNRS, Montpellier) of “Carlos 50 ”, a Conference in honor of Carlos
Simpson’s 50th birthday, IHP Paris. List of Speakers : A. Beauville (CNRS, Nice), D.
Gaitsgory (Harvard), P. Griffiths (IAS), N. Hitchin (Oxford), M. Kapranov (Yale), M.
Kontsevich (IHES), L. Katzarkov (Miami&Wien), T. Pantev (UPenn), C. Sabbah (Paris),
P. Schapira (Paris), B. Toën (CNRS, Montpellier), C. Voisin (Ec. Pol. Paris)
- June 15-20, 2015, member of Scientific Committee of “The mathematics of 21st century:
the vision of Alexander Grothendieck, Universit´e de Montpellier.
- November 22 - 28, 2015, Oberwolfach Seminar: Derived Geometry (organizer and
main lecturer, together with D. Calaque and T. Pantev), MFO Oberwolfach (Germany).
- June 6-10, 2016, Geometric methods in the mod p local Langlands correspondence
(organizer together with M. Harris, P. Schneider), Centro De Giorgi, Pisa, Italy.
- May 5 - May 11, 2018, Infinity-Categories, Infinity-Operads, and their Applications,
BIRS-CMO Oaxaca (Mexico), Organizers: Rune Haugseng (University of Copenaghen,
Denmark), David Gepner (Purdue University, US), Bertrand To¨en (CNRS, Toulouse,
France), Gabriele Vezzosi (Universit`a di Firenze).
- June 4 -7, 2018, A tale of Algebra and Geometry - A conference to celebrate Angelo
Vistoli’s 60th birthday, Department of Mathematics, Pisa (co-organized with Michele
Bolognesi (Montpellier), Mirella Manaresi (Bologna), Luca Migliorini (Bologna), Rita Pardini
(Pisa)).
- January 22 - May 24, 2019, Derived Algebraic Geometry, MSRI, Berkeley (California-
US); Organizers: Julie Bergner (University of California, Riverside), Bhargav Bhatt (University
of Michigan), Dennis Gaitsgory (Harvard University), David Nadler (University of
California, Berkeley), Nikita Rozenblyum (University of Chicago), Peter Scholze (Universit
¨at Bonn), Gabriele Vezzosi (Universit`a di Firenze).
TEACHING and ADVANCED TEACHING
- March 1997, Dept. of Mathematics, Harvard University, Lectures on “K-theory, Intersection
theory and the Grothendieck- Riemann-Roch theorem”;
- October 2000 - January 2001, PhD Course “Algebraic Geometry”, Dipartimento di
Matematica, Universita’ di Bologna - Italy.
- April 2001, Maitre de Conferences invit´e (1 month) at the Institut Fourier, Grenoble,
France;
- June 2001, Maitre de Conferences invit´e (1 month), Department de Mathematique
(Laboratoire J. Dieudonn´e) Universit´e de Nice, France;
- January-April, 2003, Tutoring for the Course Geometry and Linear Algebra, Universit`
a di Bologna - Italy;
- November 2003-February 2004, Exercises’ and Exams sessions for the Course Geometry
and Linear Algebra, electronic Engineering School, Universit`a di Firenze - Italy;
- September 2004 - December 2012, Course Geometry and Linear Algebra, School of
Engineering and Informatics & School of Environmental Engineering, Universit`a di Firenze
- Italy.
- 1-5 June, 2009, invited series of lectures on Derived Algebraic Geometry (i-MATH
School on Derived Algebraic Geometry), Instituto Universitario de Fisica Fundamental y
Matematicas, IUFFyM, Salamanca, Spain.
- July 12 - August 02, 2009, Dacha Seminar Lectures on Recent Developments in Derived
Algebraic Geometry (Speakers: B. Toen, G. Vezzosi), Steklov Institute, Moscow,
Russia.
- September 7-12, 2009, invited series of lectures at Advanced School on Homotopy
Theory and Algebraic Geometry, Mathematical Research Institute, University of Sevilla
(IMUS), Sevilla, Spain.
- September 2009 - current, Course Algebraic Coding Theory, School of Engineering
and Informatics, Universit`a di Firenze - Italy.
- 2010-2011, Third year Course Introduzione alla Geometria Di↵erenziale, School of
Engineering and Informatics, Universit`a di Firenze - Italy.
- April 2011 - PhD Course DG-categories (joint with B. To¨en), Math. Dept. Universit`a
di Padova, Italy.
- January 2013- May 2013, Cours&TD MM2 (Analyse et alg`ebre elementaires), Licence
1, Universit´e Paris Diderot, Paris, France.
- September 2013- October 2013, Cours& TD, G´eom´etrie Di↵´erentielle, Master 2, Universit
´e Paris Diderot, Paris, France.
- January 2014- May 2014, Cours&TD MM2 (Analyse et alg`ebre elementaires), Licence
1, Universit´e Paris Diderot, Paris, France.
- March 2014- May 2014, Cours & TD, Espaces de modules et prefaisceaux simpliciaux,
Master 2, Universit´e Paris Diderot, Paris, France.
- 2014-current, Geometry, 1st year, School of Mechanical Engineering, Università di
Firenze - Italy.
- 2015-current, Higher Geometry (special topic: Sheaf cohomology via derived functors),
4th year, School of Mathematics, Università di Firenze - Italy.
- 2015-current, Homological algebra, sheaves and their cohomology, Graduate School of
Mathematics, Università di Firenze - Italy.
- 2019-current, Introduction to linear codes and quantum computation, School of Engineering
and Informatics, Università di Firenze - Italy.
STUDENTS' THESES
Bachelor
• Dec. 2010 - S. Frangioni (School of Informatics and Engineering - University of
Florence - Italy), Codes and algebraic curves - Bachelor Thesis.
• June 2011 - N. Papalia (School of Informatics and Engineering - University of Florence
- Italy) - Bachelor Thesis, Quantum computation and quantum information.
• October 2011 - G. Dabisias (School of Informatics and Engineering - University of
Florence - Italy), Quantum computation and Shor’s algorithm - Bachelor Thesis.
• October 2012, G. Lo Russo, (School of Informatics and Engineering - University of
Florence - Italy), Introduction to topological quantum computation - Bachelor Thesis.
• October 2012, A. Tibo, (School of Informatics and Engineering - University of Florence
- Italy), Anyons & topological quantum computation - Bachelor Thesis.
• October 2012, G. E. Pibiri, (School of Informatics and Engineering - University of
Florence - Italy), Quantum computation and Grover’s algorithm - Bachelor Thesis.
• December 2014, M. Pippi (Dip. Mat. Università di Firenze), Cobordism categories
and Atiyah’s topological quantum field theories - Bachelor Thesis.
•December 2021, L. Yang (School of Informatics and Engineering - University of Florence
- Italy), Shor's Algorithm- Bachelor Thesis.
• February 2022, M. De Simone (School of Informatics and Engineering - University of Florence
- Italy), Decoherence in Quantum Mechanics - Bachelor Thesis (coadvised with P. Verrucchi, INFN, Firenze).
• December 2023, J. Senoner (School of Informatics and Engineering - University of Florence
- Italy), Computazione quantistica: Algoritmi di Deutsch-Josza e Grover
(Quantum computation: Deutsch-Josza and Grover algorithms) - Bachelor Thesis.
• October 2024, A. Delli Colli (School of Informatics and Engineering - University of Florence
- Italy), Quantum errors and error correction techniques - Bachelor Thesis.
• October 2024, V. Sbandati (School of Mathematics- University of Florence
- Italy), Condensed mathematics and its iterations - Bachelor Thesis.
• December 2024, C. Borghini (School of Informatics and Engineering - University of Florence
- Italy), La trasformata di Fourier quantistica ed il problema del sottogruppo nascosto- Bachelor Thesis.
• February 2025, R. Naldini (School of Informatics and Engineering - University of Florence
- Italy), Protocollo BB84 - Bachelor Thesis.
Master
• June 2013, M. Porta (Paris Sud, ALGANT), Derived formal deformation theory -
Master Thesis (Mémoire M2).
• June 2013, B. Le Grignou (ENS, Paris), Derived formal deformation theory - Master
Thesis (Mémoire M2).
• June 2013, P. Vertechi (ENS, Paris), Derived loop spaces and de Rham cohomology
- Master Thesis (Mémoire M2).
• June 2013, Y. Ségalat (UPMC Paris), Introduction to derived algebraic geometry -
Master Thesis (Mémoire M2).
• June 2014, Martin Gonzalez (UPMC, Paris), Une introduction à la géométrie symplectique
derivée - Master Thesis (Mémoire M2).
• April 2018, Cipriano Jr Cioffo (Università di Firenze), A first introduction to infinity∞-
categories, Master Thesis.
• December 2018, Alessandro D’Angelo (Università di Pisa), Derived algebraic geometry
and the multiplicative HKR theorem, Master Thesis.
• 2019/2020, Tommaso Rossi (Università di Firenze), An overview of topological K-theory,
generalizations and applications, Master Thesis.
• 2019/2020, Pietro Gigli (Università di Firenze), From Grothendieck de Rham Theorem
to derived de Rham cohomology, Master Thesis.
• 2020/2021, Pietro Vanni (Università di Firenze), Etale cohomology and the pro-étale
site, Master Thesis.
• 2020/2021, Jonah Frébault (Sorbonne Université, Paris), Condensed mathematics,
Mémoire M2.
• 2021/2022, Matteo Montagnani (Università di Firenze), An Introduction to O-minimal structures
and some applications in Algebraic Geometry, Master Thesis.
• 2023/2024, Francesco Iacca (Università di Firenze), Condensed Mathematics and Tate Objects, Master Thesis.
PhD
• September 2011, Timo Sch¨urg (Johannes Gutenberg Universit¨at - Mainz, Germany),
Deriving Deligne-Mumford stacks with perfect obstruction theories - PhD Thesis.
• September 2013 - May 2016, Mauro Porta (Université Paris Diderot, Paris and Università
di Firenze), Derived analytic geometry, PhD Thesis (mention très honorable).
• September 2013 - September 2016, Valerio Melani (Université Paris Diderot, Paris
and Università di Firenze), Derived Poisson and derived coisotropic structures, PhD
Thesis (mention très honorable).
• November 2013 - September 2017, Martino Cantadore (Università Roma La Sapienza,
Roma), Deformations of dg-categories with applications to non commutative deformations
of derived categories of cubic fourfolds, co-advisor joint with Paolo Stellari
(Dip. Matematica, Universtà di Milano), PhD Thesis.
• September 2017 - July 2020, Massimo Pippi (Université de Toulouse) Singularity categories,
matrix factorisations and vanishing cycles, co-advised with B. Toën (CNRS,
Toulouse).
• 2019-2022, Guglielmo Nocera (SNS Pisa) Non commutative structures in the geometric
Langlands program, co-advised with Mauro Porta (IRMA, Strasbourg).
CURRENT RESEARCH GRANTS
- Gruppo Nazionale Strutture Algebriche Geometriche ed Applicazioni, INDAM - Italy.
- PRIN 2020 - Derived and underived algebraic stacks and applications, MUR - Italy.
- Membre du ANR-2017 ”CatAG - Catégorification en géométrie algébrique” (Agence
Nationale de la Recherche - France, 2017).
INTERNATIONAL EDITORIAL AND SCIENTIFIC DUTIES
- January 2017 - present: member of the Editorial Board of Journal of Homotopy and
Related Structures (http://link.springer.com/journal/40062).
- May 2014 - present: member of the Editorial Board of Rendiconti del Seminario
Matematico dell’Università di Padova (http://rendiconti.math.unipd.it/home.php?lan=english).
- July 2015 - present: member of the Editorial Board of Journal of the Institute of Mathematics
of Jussieu (http://http://journals.cambridge.org/action/displayJournal?jid=JMJ).
- May 2019. present: member of the Advisory Board of Lecture Notes in Mathematics
(Springer).
- European Research Council (ERC) Advanced Grants experts panels (field of Mathematics).
- Revisore PRIN (PRIN - Research Programs of National Relevant Interest (Italy) -
evaluator) - since 2008.
- June 2012, Reviewer for GEV01 - VQR 2004-2010 (National evaluation of research
and universities, Italy - Panel of Mathematics and Informatics).
- Referee for NSF-grants (US), Research Foundation FWO – Flanders (Belgium), Fonds
National de la Recherche AFR (Luxembourg).
- Commission de spécialistes, poste MdC en Géométrie, Université Paris Diderot (Mai-
Juin, 2013).
- Referee for Inventiones Math., Compositio Math., Duke Math. Journal, Advances in
Math., Journal of the AMS, Journal of K-theory, Journal of Topology, Math. Ann., Ann.
ENS, IMRN, Acta Math.
PAPERS
1. Theses, Lecture Notes
- G. Vezzosi, “Introduction to Riemannian Geometry”, “Introduction to Symplectic Geometry”,
“Almost integrable Hamiltonian systems”, 1993, three contributions to “Geometrical
Methods in the theory of almost-integrable Hamiltonian systems”, ENEA (National
Centre for Atomic Energy) internal publication, edited by Dr. M. Pettini (Astrophysics
Observatory, Arcetri, Firenze, Italy);
- G. Vezzosi, Geometria algebrica delle equazioni alle derivate parziali ed un punto di
vista sulla quantizzazione (Algebraic geometry of partial differential equations and a point
of view on Quantization), Degree Thesis, Dipartimento di Fisica, Universit`a di Firenze,
(Defended on October 10th 1994, Advisor: Prof. Alexandre M. Vinogradov (Moscow));
- G. Vezzosi, Groupoids in symplectic Geometry, Notes of an introductory Seminar,
preprint DFF 225/04/1995, Department of Physics, University of Florence ;
- G. Vezzosi, The Chow ring of the classifying stack of PGL3, PhD Thesis, Scuola
Normale Superiore, Pisa (defended on May 13th, 1999; Supervisor: Prof. A. Vistoli
(Bologna); Jury: Prof. E. Arbarello (SNS, Pisa), Prof. B. Totaro (DPMMS, Cambridge),
Prof. G. Tomassini (SNS, Pisa); Referees: Prof. B. Totaro (DPMMS, Cambridge), Prof.
L. Barbieri-Viale (Genova), Prof. A. Vistoli (Bologna));
- B. Toen, G. Vezzosi, From Homotopical Algebra to Homotopical Algebraic Geometry
p. 1-63, Lecture Notes for the DFG-Schwerpunkt “Globale Methoden in der Komplexen
Geometrie” Workshop, Essen 25/26 October 2002; Speakers: B. Toen, G. Vezzosi; Organizers:
H. Esnault, S. M¨uller-Stach, E. Viehweg. available at the Workshop webpage
http://www.uni-essen.de/˜mat930/homotopy.html.
2. Publications
- G. Vezzosi, Localization of differential operators and of higher order de Rham complexes,
Rendiconti del Seminario Matematico dell’Universit`a di Padova, Vol. 97 (1997), 113-
133;
- G. Vezzosi, A.M. Vinogradov, Infinitesimal Stokes’ formula for higher-order de Rham
complexes, Acta Appl. Math., Vol. 49, N. 3 (1997), 311-329;
- G. Vezzosi, On the Chow ring of the classifying stack of PGL3, Journal f¨ur die reine
und angewandte Mathematik (Crelles), 523 (2000), 1-54;
- G. Vezzosi, A. Vistoli, Higher algebraic K-theory of group actions with finite stabilizers,
Duke Math. J., 113 (2002), 1-55 ;
- G. Vezzosi, Brown-Peterson spectra in stable A^1-homotopy theory, Rendiconti del
Seminario Matematico dell’Universit`a di Padova, Vol. 106 (2001), 47-64;
- G. Vezzosi, A. M. Vinogradov, On higher order analogues of de Rham cohomology,
Differential Geometry and its Applications, 19 (2003) 29-59;
- G. Vezzosi, A. Vistoli, Higher algebraic K-theory for actions of diagonalizable groups,
Inventiones Math., 153, Number 1 (2003), p. 1-44 (DOI: 10.1007/s00222-002-0275-2); Erratum,
Inventiones Math., p. 219-224, Volume 161, Number 1 July 2005.
- S. Schr¨oer, G. Vezzosi, Existence of vector bundles and global resolutions for singular
surfaces, Compositio Mathematica, 140/3 (2004), 717-728.
- B. Toën, G. Vezzosi, From HAG to DAG: derived moduli spaces, p. 175-218, in
“Axiomatic, Enriched and Motivic Homotopy Theory”, Proceedings of the NATO Advanced
Study Institute, Cambridge, UK, (9-20 September 2002), Ed. J.P.C. Greenlees, NATO
Science Series II, Volume 131 Kluwer, 2004; also available as Preprint math.AG/0210407,
October 28, 2002.
- B. Toën, G. Vezzosi, A remark on K-theory and S-categories, Topology, 43/4 (2004),
pp. 765-791.
- B. Toën, G. Vezzosi, Homotopical algebraic geometry I: Topos theory, Advances in
Mathematics, Volume 193, Issue 2 , 1 June 2005, Pages 257-372.
- B. Toën, G. Vezzosi, “Brave New” algebraic geometry and global derived moduli spaces
of ring spectra, pp. 325-359, in “Elliptic Cohomology”, Cambridge Univ. Press, 2007, H.
Miller, D. Ravenel eds.
- B. Toën, G. Vezzosi, Homotopical Algebraic Geometry II: geometric stacks and applications,
p. 1-228, Memoirs of the American Mathematical Society, volume 193, number
902, May 2008.
- B. Toën, G. Vezzosi, A note on Chern character, loop spaces and derived algebraic
geometry , in “Algebraic Topolgy – Proc. of the 2007 Abel Symposium” - Oslo, Abel Symposia,
2009, Volume 4, 331-354, Springer Verlag, 2009.
- B. Toën, G. Vezzosi, Alg`ebres simpliciales S1-´equivariantes, th´eorie de de Rham et
th´eor`emes HKR multiplicatifs, Compositio Math., Volume 147 / Issue 06 (November 2011),
pp. 1979 - 2000.
- G. Vezzosi WHAT IS...a Derived Stack?, Notices AMS - Volume 58 Issue 07 - August
2011, pp. 955-958.
- T. Pantev, B. Toën, M. Vaquié, G. Vezzosi, Shifted Symplectic Structures, Publications
Math´ematiques de l’IHES June 2013, Volume 117, Issue 1, pp 271-328, DOI:
10.1007/s10240-013-0054-1
- T. Sch¨urg, B. Toën, G. Vezzosi, Derived algebraic geometry, determinants of perfect
complexes, and applications to obstruction theories for maps and complexes, p. 1-40,
Journal f¨ur die reine und angewandte Mathematik (Crelles Journal), Volume 2015, Issue 702
(May 2015). ISSN (Print) 0075-4102, DOI: 10.1515/crelle-2013-0037, (published Online
2013-06-20).
- B. Toën, G. Vezzosi,Caract`eres de Chern, traces ´equivariantes et g´eom´etrie alg´ebrique
d´eriv´ee, Selecta Math., April 2015, Volume 21, Issue 2, pp 449-554. DOI: 10.1007/s00029-
014-0158-6.
- Steffen Sagave, Timo Sch¨urg, G. Vezzosi, Logarithmic Derived Geometry I, Journal
of the Institute of Mathematics of Jussieu, 15 (2016), no. 2, 367-405, Published online DOI
: http://dx.doi.org/10.1017/S1474748014000322.
- G. Vezzosi, A model structures on relative dg-Lie algebroids, in “Stacks and Categories
in Geometry, Topology, and Algebra”, Contemporary Mathematics (AMS), 643 (2015).
- G. Vezzosi, Quadratic forms and Cli↵ord algebras on derived stacks, Advances in
Math., Volume 301, 161-203 (October 2016).
- D. Calaque, T. Pantev, B. Toën, M. Vaqui´e, G. Vezzosi, Shifted Poisson structures
and deformation quantization, Journal of Topology Volume 10, Issue 2, June 2017, Pages
483-584.
- B. Toën, G. Vezzosi,G´eom´etrie non-commutative, formule des traces et conducteur
de Bloch, in “Actes du 1er congr`es national de la SMF - C. Lecouvrey, ´ed.”, Séminaires et
Congrès, 31, Soc. Math. de France, p. 77-107 (2018).
- T. Pantev, G. Vezzosi, Symplectic and Poisson derived geometry and deformation
quantization, “Algebraic Geometry, Salt Lake City 2015”, Proceedings of Symposia in Pure
Mathematics, Volume: 97 (part 2) AMS; Print ISBN: 978-1-4704-3578-3; p. 405-458 (2018).
- A. Blanc, M. Robalo, B. Toën, G. Vezzosi, Motivic realizations of singularity categories
and vanishing cycles, Journal de l’Ecole Polytechnique, 5 (2018), p. 651-747.
- B. Antieau, G. Vezzosi, A remark on the Hochschild-Kostant-Rosenberg theorem in
characteristic p, to appear in Annali della Scuola Normale Superiore, October 2018, doi:
10.2422/2036-2145.201711007.
- M. Maggesi, G. Vezzosi, Some elementary remarks on lci algebraic cycles, Riv. Mat.
Univ. Parma Vol. 9 (2018), 365-372.
- B. Toën, G. Vezzosi, The l-adic trace formula for dg-categories and Bloch’s conductor
conjecture, BUMI, volume 12 (2019), p. 3-17; DOI: 10.1007/s40574-018-0166-0, Springer
Verlag.
- G. Vezzosi, Basic structures on derived critical loci, Differential Geometry and Applications,
Volume 71, August 2020 - Special issue on Geometry of PDE’s - In memory of
Alexandre Mikhailovich Vinogradov, 1-12 .
- T. Pantev, G. Vezzosi, Introductory topics in derived algebraic geometry to appear
in Panorama&Synthèse, SMF (France), 2020, pp. 1-36.
- G. Vezzosi, Appendix to: D. Anderson, R. Gonzales, S. Payne, Equivariant Grothendieck-
Riemann-Roch and localization in operational K-theory, Algebra and Number Theory 15
(2021), no. 2, 341?385.
- B. Toën, G. Vezzosi, Trace and K¨unneth formulas for singularity categories and applications,
Compositio Mathematica , Volume 158 , Issue 3 , March 2022 , pp. 483 - 528
- B. Toën, G. Vezzosi, Algebraic foliations and derived geometry: the Riemann-Hilbert
correspondence, Selecta Math (2023) 29:5, p. 1-47.
- B. Toën, G. Vezzosi, Foliations and stable maps, to appear in Simons Symposia, Proceedings of the IMSA conference on "Recent Developments in Hodge Theory" (Springer), 2025, p. 1-35.
- B. Hennion, V. Melani, G. Vezzosi, A flag version of Beilinson-Drinfeld Grassmannian for surfaces, to appear in Moduli (Foundation Compositio Mathematica), 2025, p. 1-74.
3. Submitted
-V. Melani, H. Pourcelot, G. Vezzosi, Tate modules as condensed modules, Preprint arXiv:2501.07481v2, January 2025, p. 1-15.
- A. Maffei, V. Melani, G. Vezzosi, Two dimensional versions of the affine Grassmannian and their geometric description, Preprint arXiv:2503.16353, March 2025, p. 1-40.
4. Preprints
- G. Vezzosi, The Chow ring of the classifying stack of PGL(2) is generated by Chern
classes of the adjoint representation, Preprint June 1998.
- G. Vezzosi, A. M. Vinogradov, On Higher Analogs of the de Rham Complex, Preprint
ESI 202 (1995), available at ftp://ftp.esi.ac.at:/pub/Preprints/esi202.ps.
- B. To¨en, G. Vezzosi, Algebraic geometry over model categories: a general approach to
derived algebraic geometry, p. 1-52, Research announcement, Preprint math.AG/0110109,
October 10, 2001.
- G. Vezzosi, A sketchy note on enriched homotopical topologies and enriched homotopical
stacks, Preprint math.CT/0507447, July 2005, not intended for publication (available
online at http://xxx.lanl.gov/abs/math.CT/0507447).
- B. Toën, G. Vezzosi, Segal topoi and stacks over Segal sites, p. 1-22 Preprint
math.AG/0212330, December 25, 2002, contribution to Proceedings of the Program “Stacks,
Intersection theory and Non-abelian Hodge Theory”, MSRI, Berkeley, January-
May 2002.
- G. Vezzosi, A note on the cotangent complex in derived algebraic geometry, Preprint
arXiv:1008.0601, September 2010.
- D. Calaque, G. Vezzosi, The BV formalism in derived geometry, Preprint, November
2013.
- G. Vezzosi, Symmetric algebra of a cochain complex: cheat-sheet, pp. 1-14, July 2019,
Notes for students.
5. Ongoing\dormant
-B. Toen, G. Vezzosi, Derived foliations (book), 2025.
- G. Vezzosi, Formal Dirac operator on the loop space via derived algebraic and derived
analytic geometry.
- B. Toën, M. Vaquié, G. Vezzosi, Derived non abelian mixed Hodge structure with
perfect coefficients.
- B. Toën, M. Vaquié, G. Vezzosi, Deformation of dg-categories revisited, January 2012.
- G. Vezzosi, Derived singular loci II - deformations and quantization.
- G. Vezzosi, String topology on algebraic varieties via derived algebraic geometry.
- G. Vezzosi, Non abelian Hodge theory and the derived loop space.
5. Books
- Stacks and categories in Geometry, Topology and Algebra - Proceedings of CATS4,
Contemporary Mathematics, American Mathematical Society, 2015, (editor, joint with T.
Pantev, C. Simpson, B. Toën, M. Vaquié).
Standard Work address
Dipartimento di Matematica ed Informatica ’U. Dini’, Viale Morgagni, 67/a - 50134
Firenze, Italy.
E-mail: gabriele.vezzosi@unifi.it
Webpage
https://sites.google.com/unifi.it/gabriele-vezzosi/