CURRICULUM VITAE, OCTOBER Born: September 17th, 1973, in Millau (France). Citizenship: French.

Bertrand To¨en

Universit´e de Toulouse, CNRS Institut de Math´ematiques de Toulouse 118, route de Narbonne

31062 Toulouse Cedex 9 France

e-mail: bertrand.toen@math.univ-toulouse.fr

Born: September 17th, 1973, in Millau (France). Citizenship: French.

Education:

• 1991 – Baccalaur´eat – Toulouse.

• June 1996 – Master in Pure Mathematics – Universit´e de Toulouse 3

• June 1999 – Th`ese de docotorat (Ph. D.) – Universit´e de Toulouse 3

• May 2003 – Habilitation `a diriger les recherches (Habilitation thesis) – Universit´e de Nice.

Academic positions

• 1999-2001: Postdoc at Max Planck Institute f¨ur Mathematik in Bonn.

• 2001-2003: Charg´e de recherches au C.N.R.S. (permanent research posi- tion) in Laboratoire J.A. Dieudonn´e (Nice).

• 2003-2009: Charg´e de recherches au C.N.R.S. (permanent research posi- tion) in Laboratoire Emile Picard (Toulouse).

• 2009-2014: Directeur de recherches au C.N.R.S.(senior permanent research position) in Institut de Math´ematiques et de Mod´elisation de Montpellier.

• Since January 2015: Directeur de recherches au C.N.R.S.(senior permanent research position) in Institut de Math´ematiques de Toulouse.

Research interests: Algebraic Geometry, Algebraic Topology, Category The- ory.

Some distinguished lectures:

• Clay research conference, plenary talk, Oxford, September 2017.

• Premier congr`es de la Soci´et´e Math´ematique de France, plenary talk, Tours, June 2016.

• International Congress of Mathematicians, 45min lecture (section 4: Alge- braic and Complex Geometry), Seoul, August 2014.

• Alg`ebre, G´eom´etrie et Physique : une conf´erence en l’honneur de Maxim Kontsevich, IHES, Paris June 2014.

• Samuel Eilenberg Centenary Conference, plenary lecture, Warsaw, July 2013.

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• Colloque Solstice, Paris, Juin 2013.

• Derived Algebraic Geometry and Quantization, ”Whittemore Lectures”, Yale University December 2012.

• Non-Abelian Hodge theory, ”Aspects de la g´eom´etrie alg´ebrique: la prosp´erit´e math´ematique de Grothendieck”, IHES - Paris, January 2009.

Grants:

• NEDAG:”New Directions in Derived Algebraic Geometry”, ERC advanced grant (2017-2022).

• CatAG: member of ”Categorification in Algebraic geometry”, ANR grant (P.I. Etienne Mann and Michel Vaqui´e).

• DAGIT: Research grant in context of labex CIMI (2015-2018).

• HODAG:I have been the main coordinator of the grant “HODAG” (Hodge theory and derived algebraic geometry), ANR-09-BLAN-0151 (second co- ordinator C. Simpson), for the period: 2009-2013.

• GDR: I am member of the GDRalgebraic topology andalgebraic geometry.

Administration:

• Editorial works: I am currently an editor for Annales de la Facult´e des Sciences de Toulouse.

• Research administration: 2010-2014: Director of the pure math section of the Institut de Math´ematiques et de Mod´elisations de Montpellier. 2016- 2017: member of the comit´e national du CNRS, section 41. 2016-2018:

vice director of theInsitut de Math´ematiques de Toulouse.

PhD Students:

• M. Anel: thesis defended in June 2006 (Toulouse). Presently Postdoc at Paris 7.

• F. Marty: thesis defended in July 2009 (Toulouse). Presently teacher in the French school system.

• J. Wallbridge: thesis defended in July (Toulouse). Presently Postdoc at IPMU - Tokyo.

• A. Blanc: thesis defended in July 2013 (Montpellier). Presently Postdoc at Sissa.

• M. Roballo: thesis defended in July 2014 (Montpellier). Presently Maitre de conf´erences at Paris 6.

• B. Hennion: thesis defended in July 2015 (Montpellier). Presently Maitre de conf´erences at Paris 11.

• S. Bach: thesis defended in July 2017 (Montpellier).

• L. Akrout: third year PhD student in Toulouse.

• J. Antonio: third year PhD student in Toulouse.

• E. Dimitriadis: second year PhD student in Toulouse.

• M. Pippi: second year PhD student in Toulouse.

• L. Monier: first year PhD student in Toulouse.

Postdoc Students:

• Dario Beraldo (2018-2020).

• Tasos Moulinos (2018-2020).

Publications:

References

[1] Th´eor`emes de Riemann-Roch pour les champs de Deligne-Mumford.K-theory18, 1999, No.

1, 33-76.

[2] On motives for Deligne-Mumford stacks.Internat. Math. Res. Notices2000, No. 17, 909-928.

[3] Vers une interpr´etation galoisienne de la th´eorie de l’homotopie.Cah. Topol. G´eom. Diff´er.

Cat´eg.43(2002), no. 4, 257-312.

[4] (join with G. Vezzosi)A remark on K-theory and S-categories.Topology43(2004), no. 4, 765-791.

[5] (join with G. Vezzosi)From HAG to DAG: derived moduli stacks.Axiomatic, enriched and motivic homotopy theory, 173 - 216, NATO Sci. Ser. II Math. Phys. Chem., 131, Kluwer Acad. Publ., Dordrecht, 2004.

[6] (join with J. Kock)Simplicial localization of mono¨ıdal structures and a non linear version of Deligne’s conjecture.Compos. Math.141(2005), no. 1, 253-261.

[7] (join with G. Vezzosi) Homotopical Algebraic Geometry I: topos theory. Adv. Math. 193 (2005), no. 2, 257-372.

[8] Vers une axiomatisation de la th´eorie des cat´egories sup´erieures.K-Theory34(2005), no.

3, 233-263.

[9] Champs affines.Selecta Math. (N.S.)12(2006), no. 1, 39-135.

[10] Derived Hall algebras.Duke Math. J.135(2006), no. 3, 587-615.

[11] The homotopy theory of dg-categories and derived Morita theory.Invent. Math.167(2007), no. 3, 615-667.

[12] (join with Vezzosi) Brave new algebraic geometry. Elliptic cohomology, 325–359, London Math. Soc. Lecture Note Ser.,342, Cambridge Univ. Press, Cambridge, 2007.

[13] (join with M. Vaqui´e)Moduli of objects in dg-categories.Ann. Sci. Ecole Norm. Sup. (4)40 (2007), no. 3, 387-444.

[14] (join with G. Vezzosi)Homotopical algebraic geometry II: Geometric stacks and applications.

Mem. Amer. Math. Soc.193(2008), no. 902, x+224 pp.

[15] (join with L. Katzarkov et T. Pantev) Schematic homotopy types and non abelian Hodge theory, Compos. Math.144(2008), no. 3, 582-632.

[16] Anneaux de d´efinition des dg-alg`ebres propres et lisses.Bull. Lond. Math. Soc.40(2008), no. 4, 642-650.

[17] (avec M. Vaqui´e)Alg´ebrisation des vari´et´es analytiques complexes et cat´egories d´eriv´ees.

Math. Ann.342(2008), no. 4, 789-831.

[18] Finitude homotopique des dg-alg`ebres propres et lisses.Proc. Lond. Math. Soc. (3)98(2009), no. 1, 217-240.

[19] (join with M. Anel) D´enombrabilit´e des classes d’´equivalences d´eriv´ees des vari´et´es alg´ebriques.J. Algebraic Geom.18(2009), no. 2, 257-277.

[20] Higher and derived stacks: a global overview.Algebraic geometry - Seattle 2005. Part 1, 435 - 487, Proc. Sympos. Pure Math.,80, Part 1, Amer. Math. Soc., Providence, RI, 2009.

[21] (join with L. Katzarkov et T. Pantev)Algebraic and topological aspects of the schematization functor.Compos. Math. 145 (2009), no.3, 633-686.

[22] (join with M. Vaqui´e)UnderSpecZ.J. K-Theory3(2009), no. 3, 437-500.

[23] (join with G. Vezzosi)Note of Chern character, loop spaces and derived algebraic geometry.

Algebraic topology, 331-354, Abel Symp., 4, Springer, Berlin, 2009.

[24] Simplicial presheaves and derived algebraic geometry. Simplicial methods for operads and algebraic geometry, 119-186, Adv. Courses Math. CRM Barcelona, Birkh¨auser/Springer Basel AG, Basel, 2010.

[25] Lectures on dg-categories. Topics in algebraic and topological K-theory, 243-302, Lecture Notes in Math.,2008, Springer, Berlin, 2011.

[26] Descente fid`element plate pour les n-champs d’Artin. Compos. Math.147 (2011), no. 5, 1382-1412.

[27] (join with G. Vezzosi) Alg`ebres simpliciales S<sup>1</sup>-´equivariantes, th´eorie de de Rham et th´eor`emes HKR multiplicatifs.Compos. Math.147(2011), no. 6, 1979-2000.

[28] Derived Azumaya algebras and generators for twisted derived categories.Invent. Math.189 (2012), no. 3, 581-652.

[29] (join with T. Sch¨urg et G. Vezzosi)Reduced obstruction theory for the stack of stable maps to aK3-surface via derived algebraic geometry.J. Reine Angew. Math.702(2015), 1–40.

[30] (join with T. Pantev, G. Vezzosi et M. Vaqui´e)Shifted symplectic structures. Publ. Math.

Inst. Hautes ´Etudes Sci.117(2013), 271-328.

[31] (join with G. Vezzosi)Infinie-cat´egories mono¨ıdales rigides et caract`eres de Chern.To appear in Selecta.

[32] Derived Algebraic Geometry.EMS Surv. Math. Sci. 1 (2014), no. 2, 153-245.

[33] Derived Algebraic Geometry and Deformation Quantization.Proceedings of the ICM-2014.

[34] Prob`emes de modules formels. S´eminaire Bourbaki. Vol. 2015/2016. Expos´es 1104-1119.

Ast´erisque No.390(2017), Exp. No. 1111, 199-244.

[35] (join with Vaqui´e)Syst`emes de points dans les dg-cat´egories satur´ees.Ann. Fac. Sci. Toulouse Math. (6)25(2016), no. 2-3, 583–618.

[36] (Join with Calaque, Pantev, Vaqui´e and Vezzosi)Shifted Poisson Structures, J. Topol.10 (2017), no. 2, 483-584.

[37] (Join with Vezzosi)G´eom´etrie non-commutative, formule des traces et conducteur de Bloch.

Actes du 1er Congr`es National de la SMF—Tours, 2016, 77-107, S´emin. Congr., 31, Soc.

Math. France, Paris, 2017.

[38] (Join with Blanc, Robalo and Vezzosi) Matrix factorizations and vanishing cycles. J. Ec.

polytech. Math. 5 (2018), 651-747.

[39] (Join with Vezzosi)The l-adic trace formula for dg-categories and Bloch’s conductor conjec- ture.Boll. Unione Mat. Ital. 12 (2019), no. 1-2, 3-17

[40] (Join with Pantev)Poisson geometry of the moduli of local systems on smooth varieties.To appear in the Kashiwara volume, PRIMS.

Invitations to conferences

(1) International conference on intersection theory, Bologne, December 1999.

(2) Algebraic cycles, Columbus, December 2000.

(3) Orbifold String Theory, Madison, May 2001.

(4) Stacks, intersection theory and non ablian Hodge theory, MSRI, Berkeley January 2002.

(5) Great Lake K-theory Conference 8, Urbana-Champaign, April 2002.

(6) Intersection theory and Moduli, Trieste, September 2002.

(7) Axiomatic, enriched and motivic homotopy theory, Cambridge, September 2002.

(8) Moduli, Lie theory and interactions with physics, Cortona, June 2003.

(9) Homotopy Theory and its Applications, London Ontario, September 2003.

(10) Theory of motives, homotopy theory of varieties, and dessins d’enfants, Palo Alto, April 2004.

(11) N-Categories, fondations and applications, Minneapolis, June 2004.

(12) Groupoids and Stacks in Physics and Geometry, Luminy, June 2004.

(13) 24th Nordic and 1st Franco-Nordic Congress of Mathematicians, Reykjavik, January 2005.

(14) Algebraic Geometry and Categories, On the occasion of Andr´e Hirschowitz’s 61st birthday, Nice, June 2005.

(15) Conference on Algebraic Topology, Cracow, June 2005.

(16) The Arithmetic of Structured Ring Spectra, Rosendal (Norway), August 2005.

(17) Summer Institute in Algebraic Geometry, Seattle, July 2005.

(18) EMS-SCM Joint Mathematical Weekend, Barcelona, September 2005.

(19) Mathematics and its applications, SMF-UMI joint meeting, Turin, July 2006.

(20) D´eveloppements r´ecents de la th´eorie des alg`ebres de Hall, CIRM, Luminy, November 2006.

(21) G´eom´etrie alg´ebrique sur le corps `a un ´el´ement, IHES, Paris, March 2007.

(22) Derived categories, non commutative geometry and strings, Dublin, April 2007.

(23) Stacks in geometry and topology, Toronto, May 2007.

(24) Interactions with algebraic geometry, Firenze, May-June 2007.

(25) Conf´erence de g´eom´etrie alg´ebrique (en l’honneur du soixanti`eme anniver- saire d’Arnaud Beauville), Paris, June 2007.

(26) The Abel Symposium, Oslo, August 2007.

(27) Categorical aspects of algebraic geometry in mirror symmetry, RIMS, Ky- oto, D´ecember 2007.

(28) New connections of representation theory to algebraic geometry and physics, IAS, Princeton, March 2008.

(29) Conf´erence de math´ematiques du cycle scientifique du Cinquantenaire de l’IHES, IHES, Paris, May 2008.

(30) Homotopical Group Theory and Topological Algebraic Geometry, Confer- ence in honour of Haynes Miller, on the occasion of his 60th birthday, Bonn, June 2008.

(31) Homotopy Structures in Geometry and Algebra; Derived Categories, Higher Categories, CRM, Barcelona, July 2008.

(32) Workshop on triangulated categories, Swansea, D´ecember 2008.

(33) Aspects de la g´eom´etrie alg´ebrique: la post´erit´e math´ematique de Grothendieck, IHES, January 2009.

(34) Noncommutative Geometry, Arithmetic and Related Topics, Baltimore, March 2009.

(35) Topological Field Theory, Evanston, May 2009.

(36) New directions in the model theory of fields, Durham, July 2009.

(37) Derived Categories in Algebra, Topology and Geometry, Leicester, Septem- ber 2009.

(38) Workshop on mirror symmetry, Miami, January 2010.

(39) Derived categories Tokyo, January 2011.

(40) Espaces, groupes et alg`ebres de lacets, CIRM, Luminy, May-June 2011.

(41) Arakelov geometry and K-theory: On the occasion of C. Soul´e ’s 60th birth- day, Toulouse, May 2012.

(42) Rencontre ”GAC”, CIRM, Luminy, January 2013.

(43) Conference on Homological Mirror Symmetry, Miami, January 2013.

(44) Third Latin Congress on Symmetries in Geometry and Physics, Maranhao, February 2013.

(45) Operads and deformation theory, Cambridge, April 2013.

(46) The Geometry of Topological D-branes, Categories and Applications, ESI, Vienna, June 2013.

(47) Conf´erence en l’honneur de Georges Malstiniotis, Paris, June 2013.

(48) Colloque Solstice 2013, Paris, June 2013.

(49) Eilenberg Centenary Conference, Warsaw, July 2013.

(50) Derived Algebraic Geometry - Winter School, Flumserberg, November 2013.

(51) Simpson 50: A conference in honor of Carlos Simpson’s fiftieth birthday, Paris, IHP, D´ecember 2013.

(52) Alg`ebre, G´eom´etrie et Physique : une conf´erence en l’honneur de Maxim Kontsevich, IHES, Paris June 2014.

(53) Internation Congress of Mathematicians (’45), Seoul, August 2014.

(54) 6th French Philosophy of Mathematics Workshop. Toulouse, October 2014.

(55) Higher Structures 2014 Gen`eve, October 2014.

(56) Summer school on geometric Langlands and derived algebraic geometry, CIRM, Luminy, April 2015.

(57) Warwick EPSRC Symposium: Symplectic Techniques in Derived Algebraic Geometry Warwick, April 2015.

(58) GAPXIII: S´eminaire itin´erant de G´eom´etrie et Physique, IBS, Pohang, July 2015.

(59) Workshop on Derived structures in geometry and representation theory, Oxford, August 2015.

(60) Motives and Automorphic Forms, Oxford, September 2015.

(61) Topos `a l’IHES, IHES, Novemver 2015.

(62) Algebra and Geometry meeting, Barcelona, December 2015.

(63) Triangulated Categories in Algebra, Geometry and Topology, Stuttgart, March 2016.

(64) Topology of complex algebraic varieties, Luminy, May 2016.

(65) SMF 2016, Tours, June 2016.

(66) Summer school on symplectic topology, sheaves and mirror symmetry, IMJ, Paris, July 2016.

(67) Poisson 2016, Zurich-Geneva, July 2016.

(68) Non-commutative, derived and homotopical methods in geometry, Antwerp, September 2016.

(69) Homological Mirror Symmetry: emerging developments and applications, Princeton, March 2017.

(70) Derived Noncommutative Geometry, Haussdorff center, Bonn, May-June 2017.

(71) Arbeitstagung 2017 on Physical Mathematics in honor of Yuri Manin’s contributions to the field, MIPM-Bonn, June 2017.

(72) Clay Research Conference Oxford, September 2017.

(73) Algebraic Analysis, in honnor of Pierre Schapira 75th birthday, IHP Paris, April 2018.

(74) A tale of Algebra and Geometry, A conference to celebrate Angelo Vistoli’s 60th birthday, Pisa, June 2018.

(75) Higher Algebra and Mathematical Physics, Double conference Perimiter In- situte – Max Planck Insitute, August 2018.

(76) Utrecht Topology Feest 2018: in honour of Ieke Moerdijk’s 60th birthday, Utrecht, August 2018.

(77) Structures sup´erieures, CIRM, January 2019.

(78) Modern Trends in Non-Commutative Geometry (in honnor of Boris Tsy- gan’s 60th birthday), Evanston, May 2019.

Advanced courses

(1) Non-abelian cohomology, 6h, MSRI, Berkeley Janvier 2002.

(2) Homotopical algebraic geometry, 10h, Essen Octobre 2002.

(3) Lectures on dg-categories, 4h, Sedano Janvier 2007.

(4) Simplicial presheaves and derived algebraic geometry, 9h, CRM, Barcelona F´evrier 2008.

(5) Dg-categories, 4h, Padova Avril 2011.

(6) Introduction to derived algebraic geometry, 4h, Caesarea (organis´e par l’universit´e de Jerusalem), Juin 2011.

(7) Introduction to derived algebraic geometry, 3h, Grenoble (GAEL XX), Mai 2012.

(8) Shifted symplectic structures, 3h, Luminy, F´evrier 2013.

(9) Derived Algebraic Geometry - Winter School, Flumserberg, November 2013.

(10) The XIVth Summer Lectures in Geometry, Lisboa, Juin 2014.

(11) Summer school on geometric Langlands and derived algebraic geometry, CIRM, Luminy, Avril 2015.

(12) Triangulated Categories in Algebra, Geometry and Topology, Stuttgart, March 2016.

(13) Non-commutative Hodge structures, Bonn, May 2017.

(14) Pedagogical workshop on higher geometry and applications. KIAS, July 2017.

(15) Lectures on higher structures and quantisation, IPMU Tokyo, March 2018.