Moduli spaces of vector bundles on a curve and opers

Autor: Biswas, Indranil, Hurtubise, Jacques, Roubtsov, Vladimir

Let $X$ be a compact connected Riemann surface of genus $g$, with $g\, \geq\,2$, and let $\xi$ be a holomorphic line bundle on $X$ with $\xi^{\otimes 2}\,=\, {\mathcal O}_X$. Fix a theta characteristic $\mathbb L$ on $X$. Let ${\mathcal M}_X(r,\xi)$

Externí odkaz: http://arxiv.org/abs/2303.09701

Poisson and Symplectic structures, Hamiltonian action, momentum and reduction

Autor: Roubtsov, Vladimir, Dutykh, Denys

This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the Poisson and

Externí odkaz: http://arxiv.org/abs/2003.14173

Monge-Amp\`ere Structures and the Geometry of Incompressible Flows

Autor: Banos, Bertrand, Roubtsov, Vladimir, Roulstone, Ian

We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Amp\`ere structure, and Burgers'-type vortices are a canonical class of solutions associated with this structure. The ma

Externí odkaz: http://arxiv.org/abs/1510.02327

Relativistic Toda Chain with Boundary Interaction at Root of Unity

Autor: Iorgov, Nikolai, Roubtsov, Vladimir, Shadura, Vitaly, Tykhyy, Yuri

Publikováno v: SIGMA 3 (2007), 013, 14 pages

We apply the Separation of Variables method to obtain eigenvectors of commuting Hamiltonians in the quantum relativistic Toda chain at a root of unity with boundary interaction.
Comment: This is a contribution to the Vadim Kuznetsov Memorial Iss

Externí odkaz: http://arxiv.org/abs/nlin/0701040

Double Poisson brackets on free associative algebras

Autor: Odesskii, Alexander, Roubtsov, Vladimir, Sokolov, Vladimir

Publikováno v: Noncommutative birational geometry, representations and combinatorics
Contemporary Mathematics
Noncommutative Birational Geometry, Representations and Combinatorics
Arkady Berenstein, Vladimir Retakh. Noncommutative Birational Geometry, Representations and Combinatorics, 592, American Mathematical Society, pp.225-239, 2013, Contemporary Mathematics ; 592, 978-0-8218-8980-0. ⟨10.1090/conm/592⟩

We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with an associative version of Young-Baxter equations, we study a bi-hamil

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d37e770ce2ba525772d19570cd0bcf76
https://hdl.handle.net/21.11116/0000-0004-1BFA-521.11116/0000-0004-1BFC-3