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CV

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 PGL_3''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 Dipartimentodi Matematica dell'Università di Bologna, on the Project ``Intersection Theory'';- 26 February 2001, Qualification as Maitre de Conferences (Section 25 -Mathematiques) by Ministère de l'Education Nationale (France);- February 2003, winner of an Assistant Professor (Ricercatore) position in Geometry (MAT-03), Facoltà di Ingegneria, Università 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'Università 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 à Professeur by Ministère 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.- May 15, 2012, qualified first in Concours à Professeur, Université Diderot - Paris 7, Paris, France - January 2013 - resigned July 2014, Professeur at Institut de Mathématiques de Jussieu, Université 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

- 1996-now: member of G.N.S.A.G.A (Gruppo Nazionale Strutture Algebriche eGeometriche e Applicazioni) INDAM group;- 1997, Spring Semester: visiting fellow all'Harvard Department ofMathematics (Cambridge, Boston, Mass., USA);- February 10 - March 1, 1999: Visiting Fellow at Department of Mathematics andMathematical 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 invité (1 month) at the Institut Fourier,Grenoble, France;- June 2001, Maitre de Conferences invité (1 month) at Department deMathematique, Laboratoire J. Dieudonné Université 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 Fachbereich Mathematik und Informatik, Westf"alische Wilhelms-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, Dept. de Mathématiques, Université Paul Sabatier, Toulouse, France.- May 2009, invited professor at Mathematisches Institut der Universit"at Bonn.- November 2010, visitor at I3M, Université 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 Galiei 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.

INVITED TALKS

- October 3-8, 1994: invited talk ``On higher de Rham complexes'' all'``International Conference on Secondary Differential Calculus and NonlinearProblems in Physics'', Vietri sul Mare, Italy;- 29 August- 4 September 1999: Conference ``Proprietà geometriche dellevarietà 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 ofPGL_3'' 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 mathrmPGL_3'';- April 1- April 5 2000, invited talk at University of Missouri atColumbia (MO-USA), ``Classifying spaces in Algebraic Geometry'';- June 22-23, 2000: 2 invited talks ``Introduction tomathbbA^1-homotopy theory'', ``Some open problems inmathbbA^1-homotopy theory'', Dipartimento di Matematicadell'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 inmathbbA^1-homotopy theory'', ``Higher equivariant algebraicK-theory of group actions with finite stabilizers'' and ``Higheralgebraic equivariant K-theory for diagonalizable group schemes'';- June 14, 21, 2001, Nice, Laboratoire J. A. Dieudonné: invited talk ``Higheralgebraic 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 Hélène Esnault, Stefan M"uller-Stach, Eckart Viehweg). Informations and nots available at: textsfhttp://www.uni-essen.de/textrm~textsfmat930/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 textsfhttp://www.newton.cam.ac.uk/webseminars/pg+ws/NSTW04/201202/vezzosi/ ;- 17-25, May 2003 - Laboratoire J. Dieudonné, 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 metà periodo del progetto MIUR - Geometria delle Varietà 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., Université 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, Insitute for Advanced Study, Princeton, USA.- May 13-20, 2007, invited speaker allo 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, Insitute 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 onDerived Algebraic Geometry), Instituto Universitario de Fisica Fundamental y Matemàticas, 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 (première 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 (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 Géométrie, 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, 2010, 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 S?minaire Caen Cergy Clermont Paris - Théorie des Représentations, An overview of derived geometry, Batiment Sophie Germain, Universit? Paris Diderot, Paris.- April 17, 2014, invited talk Université de Montpellier 2, First steps in derived logarithmic geometry.- March 2015, invited speaker at Conference “Derived categories, Chow groups and algebraic cycles”, Special Program 'Topology of algebraic varieties', Insitute 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).

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 andassociated C^*-algebras'', ``Spectra of abelian categories andGabriel-Rosenberg reconstruction theorems for general schemes'', in the Program ``Introduction to Non-Commutative Geometry'', Scuola NormaleSuperiore, Pisa (organized by Prof. G. Tomassini, SNS, Pisa) - Italy;- November 1999, Dipartimento di Matematica, Università di Trento, seriesof 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-MATHSchool on Derived Algebraic Geometry), Instituto Universitario de Fisica Fundamental yMatematicas, IUFFyM, Salamanca, Spain.- July 12 - August 02, 2009, Dacha Seminar on Recent Developments in DerivedAlgebraic Geometry (Speakers: B. Toen, G. Vezzosi), Steklov Institute, Moscow, Russia.- September 7-12, 2009, invited series of lectures at "Advanced School on Homotopy Theoryand 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, S?minaire Autour de la G?om?trie Alg?brique D?riv?e, organizer, run by my students, IMJ, Universit? Paris Diderot, Paris (webpage with Notes texttthttp://www.math.jussieu.fr/simvezzosi/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, S?minaire Algbre et topologie homotopiques, joint with G. Maltsiniotis and B. Keller, IMJ, Paris.

CONFERENCES AS AN ORGANIZER OR 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 varietà 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. To"en (CNRS, Toulouse), C. Simpson (CNRS, Nice), T. Pantev (UPenn), M. Vaquié (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?om?tries'', Institut de Math?matiques 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? Claude Bernard Lyon 1, France), R. Pandharipande (ETH-Zurich, Switzerland), J. Souto (University of Vancouver), B. Thibert (Université de Grenoble), B. Toen (Université 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. To"en (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, Université de Montpellier.

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 invité (1 month) at the Institut Fourier,Grenoble, France;- June 2001, Maitre de Conferences invité (1 month), Department deMathematique (Laboratoire J. Dieudonné) Université de Nice, France;- January-April, 2003, Tutoring for the Course Geometry and Linear Algebra, Università di Bologna - Italy;- November 2003-February 2004, Exercises' and Exams sessions for the Course Geometry and Linear Algebra, electronic Engineering School, Università di Firenze - Italy;- September 2004 - December 2012, Course Geometry and Linear Algebra, School of Engineering and Informatics & School of Environmental Engineering, Università di Firenze - Italy. Home-page: textsfhttp://poincare.dma.unifi.it/textrm~vezzosi/didattica/.- 1-5 June, 2009, invited series of lectures on Derived Algebraic Geometry (i-MATHSchool on Derived Algebraic Geometry), Instituto Universitario de Fisica Fundamental yMatematicas, IUFFyM, Salamanca, Spain.- July 12 - August 02, 2009, Dacha Seminar Lectures on Recent Developments in DerivedAlgebraic Geometry (Speakers: B. Toen, G. Vezzosi), Steklov Institute, Moscow, Russia.- September 7-12, 2009, invited series of lectures at Advanced School on Homotopy Theoryand Algebraic Geometry, Mathematical Research Institute, University of Sevilla (IMUS),Sevilla, Spain.- September 2009 - current, Course Algebraic Coding Theory, School of Engineering and Informatics, Università di Firenze - Italy.- 2010-2011, Third year Course Introduzione alla Geometria Differenziale, School of Engineering and Informatics, Università di Firenze - Italy.- April 2011 - PhD Course DG-categories (joint with B. To"en), Math. Dept. Università di Padova, Italy.- January 2013- May 2013, Cours&TD MM2 (Analyse et algbre elementaires), Licence 1, Universit? Paris Diderot, Paris, France.- September 2013- October 2013, Cours& TD, Géométrie Différentielle, Master 2, Université Paris Diderot, Paris, France.- January 2014- May 2014, Cours&TD MM2 (Analyse et algbre elementaires), Licence 1, Université Paris Diderot, Paris, France.- March 2014- May 2014, Cours&TD, Espaces de modules et prefaisceaux simpliciaux, Master 2, Université Paris Diderot, Paris, France.

STUDENTS

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. Universit? di Firenze), Cobordism categories and Atiyah's topological quantum field theories - Bachelor Thesis.

Master- June 2013, M. Porta (Paris Sud, ALGANT), Derived formal deformation theory - Master Thesis (M?moire M2). - June 2013, B. Le Grignou (ENS, Paris), Derived formal deformation theory - Master Thesis (M?moire M2).- June 2013, P. Vertechi (ENS, Paris), Derived loop spaces and de Rham cohomology - Master Thesis (M?moire M2).- June 2013, Y. Ségalat (UPMC Paris), Introduction to derived algebraic geometry - Master Thesis (M?moire M2).- June 2014, Martin Gonzalez (UPMC, Paris), Une introduction ? la g?om?trie symplectique deriv?e - Master Thesis (M?moire M2).

PhD- September 2011, T. Sch"urg (Johannes Gutenberg Universit"at - Mainz, Germany), Deriving Deligne-Mumford stacks with perfect obstruction theories - PhD Thesis.- September 2013 - ongoing, Valerio Melani (Universit? Paris Diderot, Paris), Derived Poisson and derived coisotropic strucures, PhD Thesis.- September 2013 - ongoing, Mauro Porta (Université Paris Diderot, Paris), Derived analytic geometry, derived GAGA theorems, and non abelian mixed Hodge structures, PhD Thesis.- November 2013 -ongoing, Martino Cantadore (Universit? 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, Universt? di Milano), PhD Thesis.

RESEARCH GRANTS

- Gruppo Nazionale Strutture Algebriche Geometriche ed Applicazioni, INDAM - Italy.- MIUR - PRIN 2008 - Geometria delle varietà algebriche e dei loro spazi di moduli, Italy.- Grant ANR ANR-09-BLAN-0151 (Agence Nationale de la Recherche - France), name of project: HODAG - Projet Blanc ANR ``Géométrie Algébrique Dérivée, n-Catégories et Théorie de Hodge'' (2009-2013), project members: H. Bacard (Nice), C. Berger (Nice), André Hirschowitz (Nice), L. Katzarkov (Miami), T. Pantev (UPenn), C. Simpson (CNRS-Nice), B. To"en (CNRS-Montpellier), M. Vaquié (CNRS-Toulouse), G. Vezzosi (Firenze), J. Wallbridge (Sydney-Toulouse).

INTERNATIONAL EDITORIAL AND SCIENTIFIC DUTIES

- 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).- 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 Ð Flanders (Belgium), Fonds National de la Recherche AFR (Luxembourg). - Commission de spécialistes, poste MdC en Geomé?trie, Universit?é 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.

PAPERS

1. Theses and Lecture Notes- G. Vezzosi, ``Introduction to Riemannian Geometry'', ``Introductionto Symplectic Geometry'', ``Almost integrable Hamiltonian systems'', 1993,three contributions to ``Geometrical Methods in the theory ofalmost-integrable Hamiltonian systems'', ENEA (National Centre for AtomicEnergy) internal publication, edited by Dr. M. Pettini (AstrophysicsObservatory, Arcetri, Firenze, Italy);- G. Vezzosi, Geometria algebrica delle equazioni alle derivateparziali ed un punto di vista sulla quantizzazione (Algebraic geometryof partial differential equations and a point of view on Quantization),Degree Thesis, Dipartimento di Fisica, Università di Firenze, (Defended on October 10th 1994, Advisor: Prof. Alexandre M. Vinogradov (Moscow));- G. Vezzosi, Groupoids in symplectic Geometry, Notes of anintroductory Seminar, preprint DFF 225/04/1995, Department of Physics,University of Florence ;- G. Vezzosi, The Chow ring of the classifying stack of PGL_3,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 textsfhttp://www.uni-essen.de/textrm~textsfmat930/homotopy.html.

2. Publications- G. Vezzosi, Localization of differential operators and of higherorder de Rham complexes, Rendiconti del Seminario Matematicodell'Università di Padova, Vol. 97 (1997), 113-133;- G. Vezzosi, A.M. Vinogradov, Infinitesimal Stokes' formula forhigher-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 PGL_3,Journal f"ur die reine und angewandte Mathematik (Crelles), 523(2000), 1-54; - G. Vezzosi, A. Vistoli, Higher algebraic K-theoryof group actions with finite stabilizers, Duke Math. J., 113(2002), 1-55 ;- G. Vezzosi, Brown-Peterson spectra in stableA^1-homotopy theory, Rendiconti del Seminario Matematico dell'Università 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 algebraicK-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. To"en, 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 131Kluwer, 2004; also available as Preprint textsfmath.AG/0210407, October 28, 2002.- B. To"en, G. Vezzosi, A remark on K-theory and S-categories, Topology, 43/4 (2004),pp. 765-791.- B. To"en, G. Vezzosi, Homotopical algebraic geometry I: Topos theory, Advances in Mathematics, Volume 193, Issue 2 , 1 June 2005, Pages 257-372.- B. To"en, 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. To"en, 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. To"en, G. Vezzosi, A note on Chern character, loop spaces and derived algebraic geometry , Algebraic Topolgy -- Proc. of the 2007 Abel Symposium- Oslo, Abel Symposia, 2009, Volume 4, 331-354, Springer Verlag, 2009.- B. To"en, G. Vezzosi, Algèbres simpliciales S^1-équivariantes, théorie de de Rham et théorèmes 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. To"en, M. Vaquié, G. Vezzosi, Shifted Symplectic Structures, Publications Mathématiques de l'IH?S June 2013, Volume 117, Issue 1, pp 271-328, DOI: 10.1007/s10240-013-0054-1- T. Sch"urg, B. To"en, G. Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes, p. 1-42, Journal f"ur die reine und angewandte Mathematik (Crelles Journal), ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle-2013-0037, (published Online 2013-06-20).- B. To"en, G. Vezzosi,Caractres de Chern, traces équivariantes et géométrie algébrique dérivée, pp. 1-84, Final version April 2014, to appear in Selecta Math, DOI: 10.1007/s00029-014-0158-6.- Steffen Sagave, Timo Sch"urg, G. Vezzosi, Logarithmic Derived Geometry I, Preprint arXiv:1307.4246, Final version April 2014, to appear in Journal of the Institute of Mathematics of Jussieu. Published online DOI : http://dx.doi.org/10.1017/S1474748014000322 - G. Vezzosi, A model structures on relative dg-Lie algebroids, Preprint textttarXiv:1304.6049, final version September 2014, to appear in Proceedings of CATS4- Stacks and categories in Geometry, Topology and Algebra, CIRM Luminy, AMS (2015).

3. Submitted- G. Vezzosi, Quadratic forms and Clifford algebras on derived stacks, Preprint texttt arXiv:1309.1879, September 2013; submitted.

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 RhamComplex, Preprint ESI 202 (1995), available at textttftp://ftp.esi.ac.at:/pub/Preprints/esi202.ps.- B. To"en, G. Vezzosi, Algebraic geometry over modelcategories: a general approach to derived algebraic geometry, p. 1-52, Research announcement, Preprint textttmath.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 texttthttp://xxx.lanl.gov/abs/math.CT/0507447).- B. To"en, 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.- G. Vezzosi, Derived critical loci I - Basics, Preprint arXiv:1109.5213, August 2011.

- G. Vezzosi, M. Porta, Infinitesimal and square-zero extensions of simplicial algebras, arXiv:1310.3573, October 2013- D. Calaque, T. Pantev, B. To"en, M. Vaquié, G. Vezzosi, Shifted Poisson structures and quantization, ongoing.

5. Books- Stacks and categories in Geometry, Topology and Algebra - Proceedings of CATS4, Contemporary Mathematics, American Mathematical Society, 2015, to appear (editor, joint with T. Pantev, C. Simpson, B. Toen, M. Vaquié).

Mathematicians who may be asked about my work:

Kevin Costello (Northwestern University - Chicago - USA)Dmitry Kaledin (Steklov Institute, Moscow - Russia)Mikhail Kapranov (Kavli Institute for the Physics and Mathematics of the Universe, Tokyo - Japan)Maxim Kontsevich (IHES, Bures sur Yvette - France)Jacob Lurie (Harvard, Boston - USA)Carlos Simpson (CNRS, Nice - France)Richard Thomas (Imperial College, London - UK)Angelo Vistoli (SNS, Pisa - Italy)

- 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 PGL_3'' 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 dell'Università di Bologna, on the Project ``Intersection Theory''; - 26 February 2001, Qualification as Maitre de Conferences (Section 25 -Mathematiques) by Ministère de l'Education Nationale (France); - February 2003, winner of an Assistant Professor (Ricercatore) position in Geometry (MAT-03), Facoltà di Ingegneria, Università 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'Università 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 à Professeur by Ministère 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. - May 15, 2012, qualified first in Concours à Professeur, Université Diderot - Paris 7, Paris, France - January 2013 - resigned July 2014, Professeur at Institut de Mathématiques de Jussieu, Université Diderot - Paris 7, Paris, France. - July 2014- present, Full Professor of Geometry, Dipartimento di Matematica ed Informatica `` Ulisse Dini'' Università di Firenze (Italy).

- 1996-now: member of G.N.S.A.G.A (Gruppo Nazionale Strutture Algebriche e Geometriche e Applicazioni) INDAM group; - 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 invité (1 month) at the Institut Fourier, Grenoble, France; - June 2001, Maitre de Conferences invité (1 month) at Department de Mathematique, Laboratoire J. Dieudonné Université 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 Fachbereich Mathematik und Informatik, Westf"alische Wilhelms-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, Dept. de Mathématiques, Université Paul Sabatier, Toulouse, France. - May 2009, invited professor at Mathematisches Institut der Universit"at Bonn. - November 2010, visitor at I3M, Université 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 Galiei 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.

- 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 varietà 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 PGL_3'' 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 mathrmPGL_3''; - 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 mathbbA^1-homotopy theory'', ``Some open problems in mathbbA^1-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 mathbbA^1-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. Dieudonné: 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 Hélène Esnault, Stefan M"uller-Stach, Eckart Viehweg). Informations and nots available at: textsfhttp://www.uni-essen.de/textrm~textsfmat930/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 textsfhttp://www.newton.cam.ac.uk/webseminars/pg+ws/NSTW04/201202/vezzosi/ ; - 17-25, May 2003 - Laboratoire J. Dieudonné, 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 metà periodo del progetto MIUR - Geometria delle Varietà 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., Université 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, Insitute for Advanced Study, Princeton, USA. - May 13-20, 2007, invited speaker allo 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, Insitute 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 Matemàticas, 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 (première 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 (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 Géométrie, 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, 2010, 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 S?minaire Caen Cergy Clermont Paris - Théorie des Représentations, An overview of derived geometry, Batiment Sophie Germain, Universit? Paris Diderot, Paris. - April 17, 2014, invited talk Université de Montpellier 2, First steps in derived logarithmic geometry. - March 2015, invited speaker at Conference “Derived categories, Chow groups and algebraic cycles”, Special Program 'Topology of algebraic varieties', Insitute 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).

- 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, S?minaire Autour de la G?om?trie Alg?brique D?riv?e, organizer, run by my students, IMJ, Universit? Paris Diderot, Paris (webpage with Notes texttthttp://www.math.jussieu.fr/simvezzosi/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, S?minaire Algbre et topologie homotopiques, joint with G. Maltsiniotis and B. Keller, IMJ, Paris.

- 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 varietà 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. To"en (CNRS, Toulouse), C. Simpson (CNRS, Nice), T. Pantev (UPenn), M. Vaquié (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?om?tries'', Institut de Math?matiques 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? Claude Bernard Lyon 1, France), R. Pandharipande (ETH-Zurich, Switzerland), J. Souto (University of Vancouver), B. Thibert (Université de Grenoble), B. Toen (Université 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. To"en (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, Université de Montpellier.

- 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 invité (1 month) at the Institut Fourier, Grenoble, France; - June 2001, Maitre de Conferences invité (1 month), Department de Mathematique (Laboratoire J. Dieudonné) Université de Nice, France; - January-April, 2003, Tutoring for the Course Geometry and Linear Algebra, Università di Bologna - Italy; - November 2003-February 2004, Exercises' and Exams sessions for the Course Geometry and Linear Algebra, electronic Engineering School, Università di Firenze - Italy; - September 2004 - December 2012, Course Geometry and Linear Algebra, School of Engineering and Informatics & School of Environmental Engineering, Università di Firenze - Italy. Home-page: textsfhttp://poincare.dma.unifi.it/textrm~vezzosi/didattica/. - 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, Università di Firenze - Italy. - 2010-2011, Third year Course Introduzione alla Geometria Differenziale, School of Engineering and Informatics, Università di Firenze - Italy. - April 2011 - PhD Course DG-categories (joint with B. To"en), Math. Dept. Università di Padova, Italy. - January 2013- May 2013, Cours&TD MM2 (Analyse et algbre elementaires), Licence 1, Universit? Paris Diderot, Paris, France. - September 2013- October 2013, Cours& TD, Géométrie Différentielle, Master 2, Université Paris Diderot, Paris, France. - January 2014- May 2014, Cours&TD MM2 (Analyse et algbre elementaires), Licence 1, Université Paris Diderot, Paris, France. - March 2014- May 2014, Cours&TD, Espaces de modules et prefaisceaux simpliciaux, Master 2, Université Paris Diderot, Paris, France.

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. Universit? di Firenze), Cobordism categories and Atiyah's topological quantum field theories - Bachelor Thesis.

Master - June 2013, M. Porta (Paris Sud, ALGANT), Derived formal deformation theory - Master Thesis (M?moire M2). - June 2013, B. Le Grignou (ENS, Paris), Derived formal deformation theory - Master Thesis (M?moire M2). - June 2013, P. Vertechi (ENS, Paris), Derived loop spaces and de Rham cohomology - Master Thesis (M?moire M2). - June 2013, Y. Ségalat (UPMC Paris), Introduction to derived algebraic geometry - Master Thesis (M?moire M2). - June 2014, Martin Gonzalez (UPMC, Paris), Une introduction ? la g?om?trie symplectique deriv?e - Master Thesis (M?moire M2).

PhD - September 2011, T. Sch"urg (Johannes Gutenberg Universit"at - Mainz, Germany), Deriving Deligne-Mumford stacks with perfect obstruction theories - PhD Thesis. - September 2013 - ongoing, Valerio Melani (Universit? Paris Diderot, Paris), Derived Poisson and derived coisotropic strucures, PhD Thesis. - September 2013 - ongoing, Mauro Porta (Université Paris Diderot, Paris), Derived analytic geometry, derived GAGA theorems, and non abelian mixed Hodge structures, PhD Thesis. - November 2013 -ongoing, Martino Cantadore (Universit? 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, Universt? di Milano), PhD Thesis.

- Gruppo Nazionale Strutture Algebriche Geometriche ed Applicazioni, INDAM - Italy. - MIUR - PRIN 2008 - Geometria delle varietà algebriche e dei loro spazi di moduli, Italy. - Grant ANR ANR-09-BLAN-0151 (Agence Nationale de la Recherche - France), name of project: HODAG - Projet Blanc ANR ``Géométrie Algébrique Dérivée, n-Catégories et Théorie de Hodge'' (2009-2013), project members: H. Bacard (Nice), C. Berger (Nice), André Hirschowitz (Nice), L. Katzarkov (Miami), T. Pantev (UPenn), C. Simpson (CNRS-Nice), B. To"en (CNRS-Montpellier), M. Vaquié (CNRS-Toulouse), G. Vezzosi (Firenze), J. Wallbridge (Sydney-Toulouse).

- 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). - 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 Ð Flanders (Belgium), Fonds National de la Recherche AFR (Luxembourg). - Commission de spécialistes, poste MdC en Geomé?trie, Universit?é 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.

1. Theses and 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, Università 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 PGL_3, 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 textsfhttp://www.uni-essen.de/textrm~textsfmat930/homotopy.html.

2. Publications - G. Vezzosi, Localization of differential operators and of higher order de Rham complexes, Rendiconti del Seminario Matematico dell'Università 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 PGL_3, 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'Università 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. To"en, 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 textsfmath.AG/0210407, October 28, 2002. - B. To"en, G. Vezzosi, A remark on K-theory and S-categories, Topology, 43/4 (2004), pp. 765-791. - B. To"en, G. Vezzosi, Homotopical algebraic geometry I: Topos theory, Advances in Mathematics, Volume 193, Issue 2 , 1 June 2005, Pages 257-372. - B. To"en, 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. To"en, 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. To"en, G. Vezzosi, A note on Chern character, loop spaces and derived algebraic geometry , Algebraic Topolgy -- Proc. of the 2007 Abel Symposium- Oslo, Abel Symposia, 2009, Volume 4, 331-354, Springer Verlag, 2009. - B. To"en, G. Vezzosi, Algèbres simpliciales S^1-équivariantes, théorie de de Rham et théorèmes 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. To"en, M. Vaquié, G. Vezzosi, Shifted Symplectic Structures, Publications Mathématiques de l'IH?S June 2013, Volume 117, Issue 1, pp 271-328, DOI: 10.1007/s10240-013-0054-1 - T. Sch"urg, B. To"en, G. Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes, p. 1-42, Journal f"ur die reine und angewandte Mathematik (Crelles Journal), ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crelle-2013-0037, (published Online 2013-06-20). - B. To"en, G. Vezzosi,Caractres de Chern, traces équivariantes et géométrie algébrique dérivée, pp. 1-84, Final version April 2014, to appear in Selecta Math, DOI: 10.1007/s00029-014-0158-6. - Steffen Sagave, Timo Sch"urg, G. Vezzosi, Logarithmic Derived Geometry I, Preprint arXiv:1307.4246, Final version April 2014, to appear in Journal of the Institute of Mathematics of Jussieu. Published online DOI : http://dx.doi.org/10.1017/S1474748014000322 - G. Vezzosi, A model structures on relative dg-Lie algebroids, Preprint textttarXiv:1304.6049, final version September 2014, to appear in Proceedings of CATS4- Stacks and categories in Geometry, Topology and Algebra, CIRM Luminy, AMS (2015).

3. Submitted - G. Vezzosi, Quadratic forms and Clifford algebras on derived stacks, Preprint texttt arXiv:1309.1879, September 2013; submitted.

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 textttftp://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 textttmath.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 texttthttp://xxx.lanl.gov/abs/math.CT/0507447). - B. To"en, 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. - G. Vezzosi, Derived critical loci I - Basics, Preprint arXiv:1109.5213, August 2011.

- G. Vezzosi, M. Porta, Infinitesimal and square-zero extensions of simplicial algebras, arXiv:1310.3573, October 2013 - D. Calaque, T. Pantev, B. Toen, M. Vaquié, G. Vezzosi, Shifted Poisson structures and deformation quantization, . arXiv:1506.03699 (June 2015).

5. Books - Stacks and categories in Geometry, Topology and Algebra - Proceedings of CATS4, Contemporary Mathematics, American Mathematical Society, 2015, to appear (editor, joint with T. Pantev, C. Simpson, B. Toen, M. Vaquié).

Algebraic Geometry

Higher stacks. Equivariant algebraic K-theory and equivariant intersection theory.Homotopical and derived algebraic geometry. Moduli spaces and derived moduli spaces.Deformation Theory. dg-derived categories. Derived non-abelian Hodge theory. Derived motives. Derived symplectic and Poisson geometry. Deformation quantization of moduli spaces. Algebraic cycles.

Algebraic Topology

Model categories. Simplicial and Segal categories. Waldhausen K-theory.Geometry over ring spectra. Topological modular forms.Arithmetic aspects of stable homotopy theory.

- G. Vezzosi, M. Porta, Infinitesimal and square-zero extensions of simplicial algebras, arXiv:1310.3573, October 2013

- D. Calaque, T. Pantev, B. Toen, M. Vaquié, G. Vezzosi, Shifted Poisson structures and deformation quantization, . arXiv:1506.03699 (June 2015).