Sklyanin Bracket and Deformation of the Calogero-Moser System

A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical equations of motion via the projection method and quantize the system.Comment: 14 pages, no figure

On L-infinity morphisms of cyclic chains

Recently the first two authors constructed an L-infinity morphism using the S^1-equivariant version of the Poisson Sigma Model (PSM). Its role in deformation quantization was not entirely clear. We give here a "good" interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors.Comment: 11 page

Formality theorems for Hochschild chains in the Lie algebroid setting

In this paper we prove Lie algebroid versions of Tsygan's formality conjecture for Hochschild chains both in the smooth and holomorphic settings. In the holomorphic setting our result implies a version of Tsygan's formality conjecture for Hochschild chains of the structure sheaf of any complex manifold and in the smooth setting this result allows us to describe quantum traces for an arbitrary Poisson Lie algebroid. The proofs are based on the use of Kontsevich's quasi-isomorphism for Hochschild cochains of R[[y_1,...,y_d]], Shoikhet's quasi-isomorphism for Hochschild chains of R[[y_1,...,y_d]], and Fedosov's resolutions of the natural analogues of Hochschild (co)chain complexes associated with a Lie algebroid.Comment: 40 pages, no figure

Detection of two new RRATs at 111 MHz

A search for pulse signals in a area with declinations of +52\degr <\delta <+55\degr was carried out on the LPA LPI radio telescope. When processing ten months of observations recorded in six frequency channels with a channel width of 415 kHz and a total bandwidth of 2.5 MHz, 22 thousand events were found with a pronounced dispersion delay of signals over frequency channels, i.e. having signs of pulsar pulses. It turned out that the found pulses belong to four known pulsars and two new rotating radio transients (RRATs). An additional pulse search conducted in 32-channel data with a channel width of 78 kHz revealed 8 pulses for the transient J0249+52 and 7 pulses for the transient J0744+55. Periodic radiation of transients was not detected. The analysis of observations shows that the found RRATs are most likely pulsars with nullings, where the proportion of nulling is greater than 99.9\%.Comment: published in Astronomy Reports, translated by Yandex translator with correction of scientific lexis, 5 pages, 2 figures, 1 tabl

Formality theorems for Hochschild complexes and their applications

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200

Derived coisotropic structures I: affine case

We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras. Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting on a $P_n$-algebra. One of our main results is an identification of the space of such coisotropic structures with the space of Maurer--Cartan elements in a certain dg Lie algebra of relative polyvector fields. To achieve this goal, we construct a cofibrant replacement of the operad controlling coisotropic morphisms by analogy with the Swiss-cheese operad which can be of independent interest. Finally, we show that morphisms of shifted Poisson algebras are identified with coisotropic structures on their graph.Comment: 49 pages. v2: many proofs rewritten and the paper is split into two part

Grothendieck-Teichm\"uller and Batalin-Vilkovisky

It is proven that, for any affine supermanifold $M$ equipped with a constant odd symplectic structure, there is a universal action (up to homotopy) of the Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}_1$ on the set of quantum BV structures (i. e.\ solutions of the quantum master equation) on $M$