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Regular version of the site
Of all publications in the section: 55
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Article
Feigin B. L., Jimbo M., Miwa T. et al. International Mathematics Research Notices. 2002. No. 23. P. 1223-1237.
Added: May 31, 2010
Article
Odesskii A., Feigin B. L. International Mathematics Research Notices. 1997. No. 11. P. 531-539.
Added: Jun 1, 2010
Article
Bufetov A. I., Dymov A. V. International Mathematics Research Notices. 2019. Vol. 2019. No. 1. P. 249-319.

 

The main result of this paper is a functional limit theorem for the sine-process. In particular, we study the limit distribution, in the space of trajectories, for the number of particles in a growing interval. The sine-process has the Kolmogorov property and satisfies the central limit theorem, but our functional limit theorem is very different from the Donsker Invariance Principle. We show that the time integral of our process can be approximated by the sum of a linear Gaussian process and independent Gaussian fluctuations whose covariance matrix is computed explicitly. We interpret these results in terms of the Gaussian free field convergence for the random matrix models. The proof relies on a general form of the multidimensional central limit theorem under the sineprocess for linear statistics of two types: those having growing variance and those with bounded variance corresponding to observables of Sobolev regularity 1/2.  

Added: Nov 23, 2017
Article
Olshanski G. International Mathematics Research Notices. 2010. No. 6. P. 1102-1166.
Added: Feb 25, 2013
Article
Buryak A., Feigin B. L., Nakajima H. International Mathematics Research Notices. 2015. No. 13.

In a recent paper, the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper, we give a very short geometrical proof of that formula.

Added: Oct 10, 2015
Article
Liviu O., Verbitsky M. International Mathematics Research Notices. 2012. No. 4. P. 894-903.

A manifold M is locally conformally Kähler (LCK), if it admits a Kähler covering with monodromy acting by holomorphic homotheties. For a compact connected group G acting on an LCK manifold by holomorphic automorphisms, an averaging procedure gives a G-invariant LCK metric. Suppose that S1 acts on an LCK manifold M by holomorphic isometries, and the lifting of this action to the Kähler cover is not isometric. We show that admits an automorphic Kähler potential, and hence (for dimℂ M > 2) the manifold M can be embedded to a Hopf manifold.

Added: Oct 24, 2012
Article
Ornea L., Verbitsky M., Vuletescu V. International Mathematics Research Notices. 2013. No. 12. P. 2809-2821.

A locally conformally Khler (LCK) manifold is a complex manifold which admits a covering endowed with a Kähler metric with respect to which the covering group acts through homotheties. We show that the blow-up of a compact LCK manifold along a complex submanifold admits an LCK structure if and only if this submanifold is globally conformally Kähler. We also prove that a twistor space (of a compact four-manifold, a quaternion-Kähler manifold, or a Riemannian manifold) cannot admit an LCK metric, unless it is Kähler.

Added: Oct 10, 2013
Article
Cheltsov I., Przyjalkowski V. V., Shramov K. International Mathematics Research Notices. 2019. Vol. 2019. No. 12. P. 3683-3703.

We study two rational Fano threefolds with an action of the icosahedral group 𝔄5. The first one is the famous Burkhardt quartic threefold, and the second one is the double cover of the projective space branched in the Barth sextic surface. We prove that both of them are 𝔄5-Fano varieties that are 𝔄5-birationally superrigid. This gives two new embeddings of the group 𝔄5 into the space Cremona group.

Added: Oct 11, 2017
Article
Leonid Rybnikov. International Mathematics Research Notices. 2018. No. 1. P. 202-235.

Cactus group is the fundamental group of the real locus of the Deligne–Mumford moduli space of stable rational curves. This group appears naturally as an analog of the braid group in coboundary monoidal categories. We define an action of the cactus group on the set of Bethe vectors of the Gaudin magnet chain corresponding to arbitrary semisimple Lie algebra g. Cactus group appears in our construction as a subgroup in the Galois group of Bethe Ansatz equations. Following the idea of Pavel Etingof, we conjecture that this action is isomorphic to the action of the cactus group on the tensor product of crystals coming from the general coboundary category formalism. We prove this conjecture in the case g=sl2 (in fact, for this case the conjecture almost immediately follows from the results of Varchenko on asymptotic solutions of the KZ equation and crystal bases). We also present some conjectures generalizing this result to Bethe vectors of shift of argument subalgebras and relating the cactus group with the Berenstein-Kirillov group of piecewise-linear symmetries of the Gelfand–Tsetlin polytope.

Added: Feb 6, 2018
Article
Kuznetsov A. G., Lunts V. International Mathematics Research Notices. 2015. No. 13.

We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category that has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity.

Added: Oct 10, 2015
Article
Khristoforov M., Klimenko A. V., Bufetov A. I. International Mathematics Research Notices. 2012. No. 21. P. 4797-4829.
Added: Nov 16, 2012
Article
Sechin P. International Mathematics Research Notices. 2017. P. 1-24.

In this article, we calculate the ring of unstable (possibly nonadditive) operations from algebraic Morava K-theory K(n)^∗ to Chow groups with ℤ_(p) -coefficients. More precisely, we prove that it is a formal power series ring on generators c_i:K(n)^∗→CH^i⊗ℤ_(p) , which satisfy a Cartan-type formula.

Added: Mar 25, 2017
Article
Dunin-Barkowski P., Orantin N., Popolitov A. et al. International Mathematics Research Notices. 2018. Vol. 2018. No. 18. P. 5638-5662.

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this problem. Then we consider the generalized case of 4-colored maps and outline the idea of the proof of the corresponding spectral curve topological recursion.

Added: Dec 22, 2016
Article
Marshall I., Etingof P., Enriquez B. International Mathematics Research Notices. 2004. Vol. 36. P. 2183-2198.
Added: Oct 30, 2010
Article
Rudakov A. N., Kac V. G. International Mathematics Research Notices. 2002. No. 19. P. 1007-1025.
Added: Nov 10, 2009
Article
Efimov A. I. International Mathematics Research Notices. 2018. No. 12. P. 3834-3869.
Added: Oct 14, 2018
Article
Cheltsov I., Park J., Won J. International Mathematics Research Notices. 2017. No. 4. P. 1179-1230.

On del Pezzo surfaces, we study effective ample ℝ -divisors such that the complements of their supports are isomorphic to 𝔸1 -bundles over smooth affine curves. All considered varieties are assumed to be algebraic and defined over an algebraically closed field of characteristic 0 throughout this article.

Added: Jul 31, 2017
Article
Loktev S., Feigin B. L. International Mathematics Research Notices. 2004. Vol. 51. P. 2719-2750.
Added: Oct 4, 2010
Article
Frenkel E., Feigin B. L. International Mathematics Research Notices. 1991. Vol. 6. P. 75-82.
Added: Jun 1, 2010
Article
Galkin S., Mellit A., Smirnov M. International Mathematics Research Notices. 2015. Vol. 2015. No. 18. P. 8847-8859.

We show that the big quantum cohomology of the symplectic isotropic Grassmanian IG(2,6) is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and stresses the need to consider the big quantum cohomology in its formulation.

Added: Oct 20, 2014