Sergei Merkulov

Lectures start on Friday 7th November in room 110 at 16:20 - 19:30.

1985-1991 Science Researcher, Department of Theoretical Problems
of the USSR Academy of Sciences, Moscow.

1992-1993   postdoc, Department of Mathematics, Odense University, Denmark.

1994-1995   Senior Lecturer, School of Mathematics and Statistics, University  of Plymouth, UK.

1995-2002  Reader, Full Professor, Department of Mathematics, University of Glasgow, UK.

2002-2013   Full Professor, Department of Mathematics, University of Stockholm, Sweden. 
2011-2012   Director of the Stockholm Mathematical Center, Sweden

2013-2025     Full Professor, Mathematics Research Unit, University of Luxembourg.

2025-             Professor, Faculty of Mathematics, The Higher School of Economics, Moscow

1993 August-September  Senior scholarship at St.John's College, Oxford University
1994 June  Isaac Newton Institute for Mathematics, Cambridge
1994 September  Erwin Shrödinger International Institute, Vienna
1995 June-August  Aarhus and Odense Universities, Denmark 
1996 August   Max-Planck-Institute for Mathematics, Bonn 
1997 June  Erwin Shrödinger International Institute, Vienna
1997 July-August  Max-Planck-Institute for Mathematics, Bonn
1998 August-September  Max-Planck-Institute for Mathematics, Bonn
1998 December  University of Leipzig, Germany
1999 March-April   I.H.E.S., France
1999 October-November  Erwin Shrödinger International Institute, Vienna.
1999 August -- 2000 July  Max-Planck-Institute for Mathematics, Bonn
2001 March-April  The Fields Institute, Toronto
2001 September-October  I.H.E.S., France
2001 June-December  Max-Planck-Institute for Mathematics, Bonn
2002, June  SNS, Pisa, Italy
2002 May-July  Max-Planck-Institute for Mathematics, Bonn
2003 December  Max-Planck-Institute for Mathematics, Bonn
2004 May     Stony Brook and CUNY, New York
2004 October    I.H.E.S., France
2005 January    Mathematical Institute, Prague.
2005 November    I.H.E.S., France.'
2006 October-November    Max-Planck-Institute for Mathematics, Bonn.
2006 December    ETH, Zurich
2007 March    Clay Mathemtical Institute, Cambridge (USA) 
2007 April    Ecole normale superieure, Paris. 
2007 October    I.H.E.S., France
2008 November-December    Max-Planck-Institute for Mathematics, Bonn
2009 August-December    Max-Planck-Institute for Mathematics, Bonn
2010 March    University of Amsterdam.
2010  October  Erwin Shrödinger International Institute, Vienna
2012 January    Max-Planck-Institute for Mathematics, Bonn
2012  May  University of Toulouse, France 
2013  August-September  Max-Planck-Institute for Mathematics, Bonn 
2014 January-February   Max-Planck-Institute for Mathematics, Bonn
2014 March  Erwin Shr\"odinger International Institute, Vienna

2019 June  Simons Center for Geometry and Physics, Stony Brook, USA
2019 January  Max-Planck-Institute for Mathematics, Bonn 
2019 October-November    I.H.E.S., France
2023 February-May    I.H.E.S., France.
2023 June    ETH in Zurich, Switzerland.

Göran Gustafsson prize, The Royal Swedish Academy of Sciences, 2003.

2025

-- S.A. Merkulov, "Gravity prop and moduli spaces $M_{g,n}$}", 
 Journal of London Mathematical Society,  volume 112, Issue 4 (2025) 38pp.   https://doi.org/10.1112/jlms.70313

-- S.A. Merkulov,  "On interrelations between graph complexes",
  International Mathematical Research Notices, Issue 2  (2025)  rnae287,    https://doi.org/10.1093/imrn/rnae287.   

-- S.A. Merkulov, "A complex of ribbon quivers and $M_{g,m}$", preprint   arXiv:2503.02020
    
 -- S.A. Merkulov, "Pre-Calabi-Yau algebras and oriented gravity properad", preprint  arXiv:2501.11158.
    
 2024

 -- Sergei Merkulov, Thomas Willwacher and Vincent Wolff,  "The oriented graph complex revisited", preprint arXiv:2411.19657. 
 To appear in  Letters in Mathematical Physics.

-- Anton Khoroshkin and Sergei Merkulov, "On deformation quantization of quadratic Poisson structures", Communications in Mathematical Physics}, volume  404 (2024)} 597-628.

2023

-- S.A. Merkulov,  "Twisting of properads", Journal of Pure and Applied Algebra, volume 227  (2023)  Issue 10, 1-47.

--  S.A. Merkulov,  "Prop of ribbon hypergraphs and strongly homotopy involutive Lie bialgebras",   International Mathematical Research Notices,  vol. 7 (2023)   5685-5727.

-- S.A. Merkulov, "From gravity to string topology", Letters in Mathematical Physics vol 113 (2023)} No.3, 23 pages.

2022

-- Assar Andersson and Sergei Merkulov,  "From deformation theory of wheeled props to classification of Kontsevich formality maps",   International Mathematical Research Notices,  vol 12 (2022)  9275-9307

-- S.A. Merkulov and M. Zivkovi\' c,  "Quantizations of Lie bialgebras, duality involution and oriented graph complexes",  Letters in Mathematical Physics, vol 112, No.13 (2022)}  22 pages.

 2021

-- S.A. Merkulov, "Grothendieck-Teichmueller group,
operads and graph complexes: a survey". In: AMS Proceedings of Symposia in Pure Mathematics, ``Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry", vol. 103 (2021) 383-445.

2020

-- S.A. Merkulov, "Multi-oriented props and homotopy algebras with branes", Letters in Mathematical Physics,  vol 110  (2020) 1425-1475

-- Sergei Merkulov and Thomas Willwacher, "Classification of universal formality maps for quantizations of Lie bialgebras", Compositio Mathematica,  vol 156 (2020)  2111-2148.

2018

-- Sergei Merkulov and Thomas Willwacher, "Deformation theory of Lie bialgebra properads". In: Geometry and Physics: A Festschrift in honour of Nigel Hitchin, Oxford University Press 2018, pp. 219-248.

-- Sergei Merkulov and Thomas Willwacher,  "An explicit two step quantization of Poisson structures and Lie bialgebras" , Communications in Mathematical  Physics vol  364} (2018),  505-578

2016

-- Ricardo Campos, Sergei Merkulov and Thomas Willwacher,  "The Frobenius properad is Koszul", Duke Mathematical Journal,  vol 165, No.1 (2016), 2921-2989.

-- S.A. Merkulov, "Formality Theorem for Quantizations of Lie Bialgebras", Letters in Mathematical Physics,  vol 106, No.2 (2016}) 169-195.

-- Anton Khoroshkin, Sergei Merkulov and Thomas Willwacher,  "On quantizable odd Lie bialgebras", Letters in Mathematical Physics, vol 106, No.9 (2016)  1199-1215.

2015

 -- Sergei Merkulov and Thomas Willwacher, "Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves", preprint   arXiv:1511.07808, 51 pp.

-- Johan Alm and Sergei Merkulov,  "Grothendieck-Teichmueller group and Poisson cohomologies", Journal of Non-commutative Geometry, vol  9, No. 1  (2015) 185-214.

2014

-- Sergei Merkulov and Thomas Willwacher,  "Grothendieck-Teichmueller and Batalin-Vilkovisky",  Letters in Mathematical Physics,  vol 104 (2014) No. 5, pp 625-634.

2011

-- S.A. Merkulov,  "Permutahedra, HKR isomorphism and polydifferential Gerstenhaber-Schack complex". In: ``Higher Structure in Geometry and Physics: In Honor of Murray Gerstenhaber and Jim Stasheff", Cattaneo, A.S.,  Giaquinto, A., Xu, P. (Eds.), Progress in Mathematics 287, XV,  (2011)  Birkhauser, Boston.

-- S.A. Merkulov,  "Operads, configuration spaces and quantization". In: ``Proceedings of Poisson 2010, Rio de Janeiro",  Bull. Braz. Math. Soc., New Series, vol 42, No. 4  (2011) 683-781.

2010

-- S.A. Merkulov,  "Graph complexes with loops and wheels". In:
  ``Algebra, Arithmetic and Geometry - Manin Festschrift" (eds. Yu. Tschinkel and Yu. Zarhin), Progress in Mathematics, Birkhauser (2010) 311-354.

-- S.A. Merkulov,  "Wheeled props in  algebra, geometry and quantization", 22 pages.  In: Proceedings of the 5th European Congress of Mathematics, Amsterdam, 14-18 July, 2008. EMS Publishing House (2010) pp. 84-114.

2009

-- M. Markl,  S. Merkulov and S. Shadrin,  "Wheeled PROPs, graph complexes and the master equation", Journal of Pure and Applied Algebra, vol  213  (2009) 496-535.

-- Sergei Merkulov and  Bruno Vallette, "Deformation theory of representations of prop(erad)s II}",  Journal fur die reine und angewandte Mathematik (Qrelle),  vol 636 (2009)  123-174.

-- Sergei Merkulov and  Bruno Vallette, "Deformation theory of representations of prop(erad)s I", Journal fur die reine und angewandte Mathematik (Qrelle)},  vol 634 (2009) 51-106.

-- S.A. Merkulov, "Lectures on props, Poisson geometry and deformation quantization", in ``Poisson Geometry in Mathematics and Physics", Contemporary Mathematics, (eds. G. Dito, J.H. Lu, Y. Maeda and A. Weinstein) AMS, vol 450 (2009), 223-257.

2008

-- S.A. Merkulov, "Exotic automorphisms of the Schouten algebra of polyvector fields", preprint  arXiv:0809.2385, 29 pages.

--  S.A. Merkulov, "Operad of formal homogeneous spaces and Bernoulli numbers", Algebra & Number Theory, vol 2, No. 4 (2008) 407-433

2006

-- S.A. Merkulov, "PROP profile of Poisson geometry",  Communications in Mathematical Physics, vol  262  (2006) 117-135.

2005

S.A.\ Merkulov,  "Nijenhuis infinity and contractible dg manifolds", Compositio Mathematica, vol  141  (2005) 1238-1254.

2004

-- S.A. Merkulov, "De Rham model for string topology",  International Mathematical Research Notices,  vol 55  (2004) 2955-2981.

--  S.A. Merkulov, "Operads, deformation theory and $F$-manifolds".
In:  Frobenius manifolds (Festschrift for Yu.I. Manin), 213--251, Aspects Math., E36, Vieweg, Wiesbaden,  (2004).

2001

-- S.A. Merkulov, "Semi-infinite A-variations of Hodge structure over extended Kaehler cone", International Mathematical Research Notices,  vol 21  (2001) 1111-1139.

-- S.A. Merlulov, "Extended complex manifolds", In: Symplectic and contact topology: interactions and perspectives (Toronto, ON/Montreal, QC, 2001), 145--155,  Fields Inst. Commun., 35, Amer. Math. Soc., Providence, RI, (2003).

2000

-- S.A. Merkulov,  "Frobenius_infty invariants of homotopy Gerstenhaber algebras I,  Duke Mathematical Journal,  vol 105 (2000) 411-461.

-- S.A. Merkulov,  "An L_infty-algebra of an unobstructed deformation functor", International  Mathematical Research Notices, vol 3  (2000) 147-164.

-- S.A. Merkulov, "The extended moduli space of
special Lagrangian submanifolds", Communications in Mathematical  Physics, vol  209  (2000) 13-27.

1999

--  S.A. Merkulov and  L. Schwachhöfer, "Classification of holonomy groups of torsion-free affine connections",    Annals of  Mathematics,  vol 150  (1999) 77-149.

-- S.A. Merkulov, "Deformation quantization of the n-tuple point,   Communications in  Mathematical Physics, vol  205 (1999) 369-375.

--  S.A. Merkulov, "Strong homotopy algebras of a Kaehler
manifold", International Mathematical Research Notices, vol 3 (1999) 153-164.

-- S. Huggett and S. Merkulov, "Twistor transform of vector bundles",  Mathematica Scandinavica, vol 85 (1999) 219-244.

1998

-- S.A. Merkulov,  "The formality of canonical symplectic complexes and Frobenius manifolds", International Mathematical Research Notices, vol 14 (1998) 727-733.

-- S. Merkulov and  L. Schwachhöfer, "Twistor solution of the holonomy problem",  in "The Geometric Universe", Oxford University Press (1998) pp. 395-402.

1997

-- Yu.I. Manin and S.A. Merkuklov, "Semisimple Frobenius (super)manifolds and quantum cohomology of $P^r$",  Topological Methods in Nonlinear Analysis, vol 9 (1997) 107-161.

--  S.A. Merkulov, "Existence and geometry of Legendre moduli spaces",  Mathematische Zeitschrift, vol 226 (1997) 211-265.

--  S.A. Merkulov, Addendum to the 2nd edition of the book "Gauge Field Theory and Complex Geometry" by Yu.I. Manin, Springer-Verlag  1997.

-- S. Merkulov and   H. Pedersen, "Projective structures on moduli spaces of compact complex hypersurfaces", Proceedings of the American Mathematical Society, vol  125  (1997) 407-416.

-- Q.-S.Chi, S.A. Merkulov and L.Schwachhöfer,  "Exotic holonomies $E^{(a)}_7$}",  International Journal of  Mathematics, vol  8, No.5 (1997) 583-594.

1996

-- S.A. Merkulov, "Classification of Segre holonomies of torsion-free affine connections", preprint MPI 96-107   (1996).

--  Q.-S. Chi, S.A. Merkulov and L.\Schwachhöfer, "On the existence of an infinite series of exotic holonomies", Inventiones Mathematicae,  vol 126 (1996) 391-411.

-- S.A. Merkulov, "Affine connections on involutive $G$-structures". In: "Geometry and Physics", Marcel Dekker, 1996, pp. 261-274.

-- S.A. Merkulov, "Geometry of Kodaira moduli spaces",   Proc. Amer. Math. Soc. vol 124 (1996)}, 1499-1506.

1995

-- S.A. Merkulov, "Moduli spaces of compact submanifolds
of complex fibred manifolds",   Math. Proc. Cambridge Phil. Soc.,
vol 118  (1995) 71-91.

1994

-- S.A. Merkulov, "Moduli of compact Legendre submanifolds of complex contact manifolds", Mathematical Research Letters, vol 1 (1994) 717-727.

-- S.A. Merkulov,  H. Pedersen and A. Swann, "Topological quantum field theory on quaternionic manifolds", Journal of Geometry and Physics,   vol 14 (1994) 121-145.

-- S.A. Merkulov, "Relative deformation theory and differential geometry". In: "Twistor Theory", Lect. Notes in Pure and Applied Math., vol. 169 (1994)  239-261.

-- S.A. Merkulov and H. Pedersen, "Geometry of relative deformations II". In: "Twistor Theory",  Lect. Notes in Pure and Applied Math., vol. 169   (1994) 239-261.

-- S.A. Merkulov, "Geometry of relative deformations I". In: "Twistor Theory",  Lect. Notes in Pure and Applied Math., vol. 169   (1994) 199-237.

1993

-- S.A. Merkulov,  "Quaternionic supermanifolds", Functional Analysis and Its Applications, vol 27, No.1  (1993) 78-80.

-- S.A. Merkulov, "Self-dual Einstein supermanifolds and supertwistor theory". In: "Spinors, Twistors, Clifford Algebras and Quantum Deformations", (Z. Oziewicz et al., eds.),
 Kluver Academic Publishers, pp. 141-146   (1993)

-- S.A. Merkulov,  "Holomorphic geometry of superstring theory",  Journal of Geometry and Physics,  vol 10  (1993) 155-174.

-- S.A. Merkulov, "Simple supergravity, supersymmetric non-linear gravitons and supertwistor theory", Classical and Quantum Gravity, vol 9  (1993) 2369-2393.

1992

-- S.A. Merkulov,  "Quaternionic, quaternionic Kaehler, and hyper-Kaehler supermanifolds", Letters in Mathematical Physics, vol  25} (1992) 7-16.

-- S.A. Merkulov, "Geometric quantization of N=2 superstring",  Journal of Mathematical Physics, vol 33, no. 9  (1992) 3159-3171.

-- S.A. Merkulov,  "On the geometric quantization of bosonic string", Classical and Quantum Gravity,  vol 9, No. 10  (1992)  2267-2276.

-- S.A. Merkulov, "Supersymmetric non-linear graviton",  Funkt. Anal. Pril. vol 26 (1992) no.\,1   [English translation in Functional Analysis and its Applications, vol  26, no. 1  (1992)  72-73].

-- S.A. Merkulov, "Non-perturbative Neveu-Schwarz superstring and Sdiff(S^1)/OSp(1| 2)",
JETP Letters, vol  55, no.3  (1992) 148-150.

--  S.A. Merkulov, "Non-perturbative bosonic string and  Diff(S^1)/SL(2,R),  JETP Letters, vol  55, no.3 (1992) 145-147.

-- S.A. Merkulov, "Superconformal geometry in three dimensions",  Journal of Mathematical Physics, vol 33, no.2  (1992) 735-757.

1991

-- S.A. Merkulov, "Quantum deformation of compactified Minkowski space",  Zeitschrift fur Physik,  vol C52  (1991) 583-588.

-- S.A. Merkulov, "Quantum $m\times n$-matrices and $q$-deformed  Binet-Cauchy formula",  Journal of Physics A: Math. & Gen. vol 24 (1991) L1243-L1247.

-- S.A. Merkulov, 'Twistor transform of Einstein-Weyl superspaces",  Classical and Quantum Gravity, vol 8 (1991) 2149-2162.

-- S.A. Merkulov, "Paraconformal supermanifolds and non-standard supergravity theories", Classical and Quantum Gravity, vol  8}  (1991) 557-569.

1990

-- S.A. Merkulov,  "Twistor transform of conformally Einstein quaternionic manifolds",  Funkt. Anal. Pril.  vol  24, no.4  (1990) 84-85 [English translation in  Functional Analysis and its Applications, vol 24, no.4  (1990) 334-335].

-- S.A. Merkulov, "Geometry of N=1 supergravity in
(mn|m+n)-dimensional superspace", Yadernaya. Fiz. vol 51, no.5  (1990) 1445-1453
[English translation in Soviet Journal of Nuclear Physics, vol 51, no.5 (1990) 915-919.]

-- S.A. Merkulov, "N=2 superconformal Einstein superspaces". Classical and Quantum Gravity, vol 7, no.3  (1990) 439-444.

1989

-- S.A. Merkulov, "Local supertwistors and N=2 conformal
supergravity".  Teor. Mat. Fiz. vol 79, no.2  (1989) 253-262 [English
translation in Theoretical and Mathematical Physics, vol 79, no.2  (1989)]
517-523].

-- S.A. Merkulov, "A conformal non-linear graviton",  Funkt. Anal. Pril. vol 23, no.3  (1989) 69-70 [English translation in Functional
Analysis and its Applications, vol  23 (1989), no.3].

-- S.A. Merkulov, "Superconformally flat superspace". Classical and Quantum Gravity, vol 6, no.10  (1989) 1433-1443.

1988

-- S.A. Merkulov,  "N=2 local supertwistors".  Classical and Quantum Gravity,  vol 5 (1988) 1373-1379.

-- S.A. Merkulov, "Conformal invariance in supersymmetric Yang-Mills theories".  Yadernaya Fiz., vol 48 (1988) 1187-1190 [English translation in Soviet Journal of Nuclear Physics, vol 48, no.4  (1988) 754-755].

-- S.A. Merkulov, "Twistors and conformally invariant fields",  Teor. Mat. Fiz. vol 77, no.2   (1988) 171-178 [English translation in Theoretical and Mathematical Physics, vol 77, no.2   (1988) 1123-1128].

1987

-- S.A. Merkulov, "N=1 local supertwistors",  Yadernaya Fiz., vol 46 (1987) 1578-1589 [English translation in  Soviet Journal of Nuclear Physics, vol 46 (1987) 937-943].

1985

-- S.A. Merkulov, "Supertwistor connection and conformal supergravity",  Teor. Mat. Fiz., vol 64, no.3  (1985) 426-431 [English translation in Theoretical and Mathematical Physics, vol 64, no.3  (1985) 933-937]

-- S.A. Merkulov, "Supersymmetric Yang-Mills theory and conformal invariance", Yadernaya Fiz., vol 42  (1985) 1279-1281 [English translation in  Soviet Journal of Nuclear Physics, vol 42, no.5  (1985) 754-755].

-- S.A. Merkulov and  N.V. Mietskievich,  "Tensor Analysis for Physicists". Moscow: PFU Press  (1985) 80 pages.

1984

-- S.A. Merkulov, "A conformally invariant theory of gravitation and electromagnetism",  Classical and Quantum Gravity,  vol 1, no.4  (1984) 349-354.

-- S.A. Merkulov, "The twistor connection and gauge invariance principle",  Communications in Mathematical Physics, vol 93, no.3  (1984) 325-331.