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From gravity to string topology
Letters in Mathematical Physics. 2023. Vol. 113. No. 3. Article 62.
Merkulov S., Journal of Pure and Applied Algebra 2023 Vol. 227 No. 10 P. 1–47
Added: December 19, 2025
Merkulov S., International Mathematics Research Notices 2023 No. 7 P. 5685–5727
Added: December 19, 2025
Merkulov S., Živković M., Letters in Mathematical Physics 2022 Vol. 112 No. 13
We prove that the action of the Grothendieck–Teichmüller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the latter. We also prove that every universal quantization of Lie bialgebras is homotopy equivalent to the one which commutes with the duality involution exchanging Lie bracket and Lie cobracket. ...
Added: December 19, 2025
Buryak A., Rossi P., International Mathematics Research Notices 2025 Vol. 2025 No. 20 Article rnaf315
The Riemann hierarchy is the simplest example of rank one, (+)-dimensional integrable system of nonlinear evolutionary PDEs. It corresponds to the dispersionless limit of the Korteweg–de Vries hierarchy. In the language of formal variational calculus, we address the classification problem for deformations of the Riemann hierarchy satisfiying different extra requirements (general deformations, deformations as systems ...
Added: November 27, 2025
Kazaryan M., Norbury P., International Mathematics Research Notices 2024 Vol. 2024 No. 3 P. 1825–1867
We construct an infinite collection of universal—independent of (g,n)—polynomials in the Miller–Morita–Mumford classes κm ∈ H2m(Mg,n, Q), defined over the moduli space of genus g stable curves with n labeled points. We conjecture vanishing of these polynomials in a range depending on g and n. ...
Added: February 19, 2024
Bolbachan V., Geometriae Dedicata 2021 No. 215 P. 443–455
To any cubic surface, one can associate a cubic threefold given by a triple cover of P3P3 branched in this cubic surface. D. Allcock, J. Carlson, and D. Toledo used this construction to define the period map for cubic surfaces. It is interesting to calculate this map for some specific cubic surfaces. In this paper, we have ...
Added: May 28, 2022
Buryak A., Clader E., Tessler R., International Mathematics Research Notices 2022 Vol. 2022 No. 14 P. 10458–10532
We lay the foundation for a version of r-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of r-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically ...
Added: October 29, 2021
Иванов А. Н., Математический сборник 2020 Т. 211 № 7 С. 72–92
We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme M(k), k≥3, of semistable rank-2 sheaves on P3 with Chern classes c1=0, c2=k and c3=0, whose general points are sheaves with singularities of mixed dimension. These sheaves are constructed by elementary transformations of stable and properly μ-semistable reflexive sheaves along disjoint unions of collections of points and smooth irreducible curves which ...
Added: October 11, 2021
Katzarkov L. V., Lupercio E., Meersseman L. et al., Advances in Mathematics 2021 Vol. 391 Article 107945
n this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the non-commutative version of the classical theory; it generalizes non-trivially most of the theorems and properties of toric geometry. By considering ...
Added: September 24, 2021
Tikhomirov A. S., Matemática Contemporânea 2020 Vol. 47 P. 301–316
In this article, we will give a review of recent results on the geography and geometry of the Gieseker-Maruyama moduli scheme M = M (c1 , c2 ) of rank 2 semi-stable coherent sheaves with first Chern class c1 = 0 or −1, second Chern class c2 , and third Chern class 0 on the ...
Added: December 22, 2020
Buryak A., Letters in Mathematical Physics 2015 Vol. 105 No. 10 P. 1427–1448
In a recent paper R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The authors conjectured KdV and Virasoro type equations that completely determine all intersection numbers. In this paper we study these equations in detail. In particular, we prove that ...
Added: September 29, 2020
Buryak A., Moscow Mathematical Journal 2016 Vol. 16 No. 1 P. 27–44
Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers is a specific solution of a system of PDEs, that they called the open KdV equations. In this paper we show ...
Added: September 28, 2020
Buryak A., Guere J., Journal de Mathématiques Pures et Appliquées 2016 Vol. 106 No. 5 P. 837–865
The double ramification hierarchy is a new integrable hierarchy of hamiltonian PDEs introduced recently by the first author. It is associated to an arbitrary given cohomological field theory. In this paper we study the double ramification hierarchy associated to the cohomological field theory formed by Witten's r-spin classes. Using the formula for the product of ...
Added: September 28, 2020
Alexandrov A., Buryak A., Tessler R., Journal of High Energy Physics 2017 Vol. 2017 No. 123 P. 123
A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J. P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction was later generalized to all genera by J. P. Solomon and the third ...
Added: September 27, 2020
Buryak A., Tessler R., Communications in Mathematical Physics 2017 Vol. 353 No. 3 P. 1299–1328
In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers satisfies the open KdV equations. In this paper we prove this conjecture. Our proof goes ...
Added: September 27, 2020
Buryak A., Clader E., Tessler R., Journal of Geometry and Physics 2019 Vol. 137 P. 132–153
We study a generalization of genus-zero r-spin theory in which exactly one insertion has a negative-one twist, which we refer to as the "closed extended" theory, and which is closely related to the open r-spin theory of Riemann surfaces with boundary. We prove that the generating function of genus-zero closed extended intersection numbers coincides with the ...
Added: September 27, 2020
Springer, 2020.
This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. ...
Added: August 13, 2020
Kazaryan M., Lando S., Prasolov V., Switzerland: Springer, 2018.
This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well.
The book begins by studying individual smooth algebraic curves, including the most beautiful ones, ...
Added: November 19, 2018
Tyurin N. A., / Series arXiv "math". 2018.
In the previous papers we present a construction of the set U_SBS in the direct product B_S×PΓ(M, L) of the moduli space of Bohr - Sommerfeld lagrangian submanifolds of fixed topological type and the projectivized space of smooth sections of the prequantization bundle L→M over a given compact simply connected symplectic manifold M. Canonical projections ...
Added: October 15, 2018
Tyurin N. A., / Series arXiv "math". 2018.
We present an example of modified moduli space of special Bohr-Sommerfeld lagrangian submanifolds for the case when the given algebraic variety is the full flag F3 for C3 and the very ample bundle is K^{-1/2}_{F3} ...
Added: October 15, 2018