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Regular version of the site
Of all publications in the section: 324
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Working paper
Entov M., Verbitsky M. math. arxive. Cornell University, 2017
Let M be a closed symplectic manifold of volume V. We say that the symplectic packings of M by ellipsoids are unobstructed if any collection of disjoint symplectic ellipsoids (possibly of different sizes) of total volume less than V admits a symplectic embedding to M. We show that the symplectic packings by ellipsoids are unobstructed for all even-dimensional tori equipped with Kahler symplectic forms and all closed hyperkahler manifolds of maximal holonomy, or, more generally, for closed Campana simple manifolds (that is, Kahler manifolds that are not unions of their complex subvarieties), as well as for any closed Kahler manifold which is a limit of Campana simple manifolds in a smooth deformation. The proof involves the construction of a Kahler resolution of a Kahler orbifold with isolated singularities and relies on the results of Demailly-Paun and Miyaoka on Kahler cohomology classes.
Working paper
Cheltsov I., Martinez-Garcia J. math. arxive. Cornell University, 2018
We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide new obstructions for the existence of constant scalar curvature Kahler metrics on polarized smooth del Pezzo surfaces.
Working paper
Déev R. N. math. arxive. Cornell University, 2015
In the present paper we prove that any family of hyperk¨ahler manifolds over a compact simply connected base can be pulled back from a family over a curve. A consimilar result about families of complex tori is also obtained.
Working paper
Klimenkova O., Menshutin A., Shchur L. math. arxive. Cornell University, 2018. No. 1811.03788.
Working paper
Frikha N., Konakov V., Menozzi S. math. arxive. Cornell University, 2019. No. 1910.05945.
We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKeanVlasov driven by non-degenerate symmetric α-stable L´evy processes with values in R^d under some mild Holder regularity assumptions on the drift and diffusion coefficients with respect to both space and measure variables. The methodology developed here allows to consider unbounded drift terms even in the so-called super-critical case, i.e. when the stability index α ∈ (0, 1). New strong well-posedness results are also derived from the previous analysis.
Working paper
Feigin E., Makedonskyi I. math. arxive. Cornell University, 2015. No. 1507.01362.
The main goal of our paper is to establish a connection between the Weyl modules of the current Lie superalgebras (twisted and untwisted) attached to osp(1,2) and the  nonsymmetric Macdonald polynomials of types $A_2^2$ and ${A_2}^{2\dagger}$  . We compute the dimensions and construct bases of the Weyl modules. We also derive explicit formulas for the t=0 and t=\infty specializations of the nonsymmetric Macdonald polynomials. We show that the specializations can be described in terms of the Lie superalgebras action on the Weyl modules