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October 8, 2026
HSE Experts Take Part in 23rd Annual Meeting of Valdai Discussion Club
The 23rd Annual Meeting of the Valdai Discussion Club was held from September 28 to October 1, 2026 under the theme ‘Responsibility for the Future: Limits of the Possible, or Limitless Possibilities?’ The forum brought together 120 experts from 40 countries, including representatives of China, the United States, India, Brazil, the United Kingdom, Germany, Egypt, Iran, and Japan.
October 7, 2026
‘Our Team Consists of True Leaders in Their Respective Academic Disciplines
The HSE International Centre of Decision Choice and Analysis studies a wide range of methods for analysing decision-making and possible scenarios for the development of natural, socio-economic, and political phenomena using various mathematical models. The application of advanced mathematical methods to forecasting helps to prevent negative outcomes and avoid erroneous decisions. The HSE News Service spoke to the centre’s director, Prof. Fuad Aleskerov, about its work.
October 6, 2026
International N5 Symposium ‘Neural Networks and Nonlinearity in Nizhny Novgorod Brings Together Scientists from Russia and Serbia
The International N5 Symposium ‘Neural Networks and Nonlinearity in Nizhny Novgorod’ was held at the Nizhny Novgorod House of Scientists from September 23 to 26. The event was organised by HSE University–Nizhny Novgorod and the Nizhny Novgorod House of Scientists, with the participation of Sberbank and the Institute of Physics Belgrade. The symposium was held for the second time: the first conference took place in 2025 and attracted considerable interest from the academic community.

 

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PROP profile of Poisson geometry

Communications in Mathematical Physics. 2006. Vol. 262. P. 117–135.
Merkulov S.
Language: English
DOI
Keywords: properads and propsPoisson bracket
Similar publications
Nijenhuis infinity and contractible dg manifolds
Merkulov S., Compositio Mathematica 2005 Vol. 141 No. 5 P. 1238–1254
Added: October 1, 2026
Deformation theory of representations of prop(erad)s I
Merkulov S., Vallette B., Journal fuer die reine und angewandte Mathematik 2009 Vol. 634 P. 51–106
Added: October 1, 2026
Deformation theory of representations of prop(erad)s II
Merkulov S., Vallette B., Journal fuer die reine und angewandte Mathematik 2009 Vol. 636 P. 123–174
Added: October 1, 2026
Wheeled PROPs, graph complexes and the master equation
Merkulov S., Shadrin S., Markl M., Journal of Pure and Applied Algebra 2009 Vol. 213 P. 496–535
Added: October 1, 2026
Grothendieck-Teichmuуller group and Poisson cohomologies
Merkulov S., Alm J., Journal of Noncommutative Geometry 2015 Vol. 9 No. 1 P. 185–215
Added: October 1, 2026
On quantizable odd Lie bialgebras,
Merkulov S., Khoroshkin A., Willwacher T., Letters in Mathematical Physics 2016 Vol. 106 P. 1199–1215
Motivated by the universal obstruction to the deformation quantization of Poisson structures in infinite dimensions we introduce the notion of quantizable odd Lie bialgebra. The main result of the paper is a construction of a highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so called ...
Added: September 30, 2026
Formality Theorem for Quantizations of Lie Bialgebras
Merkulov S., Letters in Mathematical Physics 2016 Vol. 106 No. 2 P. 169–195
Using theory of props we prove a formality theorem associated with universal quantizations of (strongly homotopy) Lie bialgebras. ...
Added: September 30, 2026
The Frobenius properad is Koszul
Merkulov S., Willwacher T., Campos R., Duke Mathematical Journal 2016 Vol. 165 No. 1 P. 2921–2989
We show the Koszulness of the properad governing involutive Lie bialgebras and also of the properads governing nonunital and unital-counital Frobenius algebras, solving a long-standing problem. This gives us minimal models for their deformation complexes, and for deformation complexes of their algebras which are discussed in detail. Using an operad of graph complexes we prove, ...
Added: September 30, 2026
Pre-Calabi-Yau algebras and oriented gravity properad
Merkulov S., Journal of Pure and Applied Algebra 2026 Vol. 230 P. 1–19
We study the dual cyclic Hochschild  complex $Cyc(A,\K)$ of a (possibly, infinite-dimensional) $A_\infty$-algebra $(A,\mu)$ and prove that any pre-Calabi-Yau extension  $\pi$ of the given $A_\infty$ structure $\mu$ in $A$ induces on the cyclic cohomology of $(A,\mu)$ a representation of a new dg properad of {\em oriented}\, ribbon graphs. We compute the cohomology of that properad in terms of ...
Added: September 29, 2026
Compatible Poisson Brackets Associated with Elliptic Curves in G(2, 5)
Nikita Markarian, Polishchuk A., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2024 Vol. 20 Article 037
We prove that a pair of Feigin–Odesskii Poisson brackets on P4 associated with elliptic curves given as linear sections of the Grassmannian G(2,5) are compatible if and only if this pair of elliptic curves is contained in a del Pezzo surface obtained as a linear section of G(2, 5). ...
Added: December 2, 2024
Elliptic zastava
Michael Finkelberg, Matviichuk M., Polishchuk A., Journal of Algebraic Geometry 2023 Vol. 32 No. 1 P. 183–237
We study the elliptic zastava spaces, their versions (twisted, Coulomb, Mirković local spaces, reduced) and relations with monowalls moduli spaces and Feigin-Odesskiı̆ moduli spaces of G-bundles with parabolic structure on an elliptic curve. ...
Added: February 26, 2023
Transposed Poisson structures on Galilean and solvable Lie algebras
Kaygorodov I., Lopatkin V., Zhang Z., / Series arXiv "math". 2022.
Transposed Poisson structures on complex Galilean type Lie algebras and superalgebras are described. It was proven that all principal Galilean Lie algebras do not have non-trivial 12-derivations and as it follows they do not admit non-trivial transposed Poisson structures. Also, we proved that each complex finite-dimensional solvable Lie algebra admits a non-trivial transposed Poisson structure and ...
Added: January 17, 2023
On Quantizable Odd Lie Bialgebras
Khoroshkin A., Mekulov S., Willwacher T., Letters in Mathematical Physics 2016 Vol. 106 No. 9 P. 1199–1215
Motivated by the obstruction to the deformation quantization of Poisson structures in infinitedimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures. ...
Added: September 11, 2016
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