National Research University – Higher School of Economics

About: National Research University – Higher School of Economics is a education organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Politics. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

Bilinear Equations on Painlevé τ Functions from CFT

Abstract: In 2012, Gamayun, Iorgov, and Lisovyy conjectured an explicit expression for the Painleve VI τ function in terms of the Liouville conformal blocks with central charge c = 1. We prove that the proposed expression satisfies Painleve VI τ function bilinear equations (and therefore prove the conjecture). The proof reduces to the proof of bilinear relations on conformal blocks. These relations were studied using the embedding of a direct sum of two Virasoro algebras into a sum of Majorana fermion and Super Virasoro algebra. In the framework of the AGT correspondence, the bilinear equations on the conformal blocks can be interpreted in terms of instanton counting on the minimal resolution of \({\mathbb{C}^2/\mathbb{Z}_2}\) (similarly to Nakajima–Yoshioka blow-up equations).

$${\mathbb{G}_a^ M}$$ degeneration of flag varieties

Abstract: Let \({\mathcal{F}_\lambda}\) be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module Vλ. We define a flat degeneration \({\mathcal{F}_\lambda^a}\) , which is a \({\mathbb{G}^M_a}\) variety. Moreover, there exists a larger group Ga acting on \({\mathcal{F}_\lambda^a}\) , which is a degeneration of the group G. The group Ga contains \({\mathbb{G}^M_a}\) as a normal subgroup. If G is of type A, then the degenerate flag varieties can be embedde‘d into the product of Grassmannians and thus to the product of projective spaces. The defining ideal of \({\mathcal{F}_\lambda}\) is generated by the set of degenerate Plucker relations. We prove that the coordinate ring of \({\mathcal{F}_\lambda^a}\) is isomorphic to a direct sum of dual PBW-graded \({\mathfrak{g}}\) -modules. We also prove that there exists bases in multi-homogeneous components of the coordinate rings, parametrized by the semistandard PBW-tableux, which are analogs of semistandard tableaux.

Do cooperative enterprises create social trust

Abstract: This article contributes to the literature by carrying out the first empirical investigation into the role of different types of enterprises in the creation of social trust. Drawing on a unique data set collected through the administration of a questionnaire to a representative sample of the population of the Italian Province of Trento in March 2011, we find that cooperatives are the only type of enterprise where the work environment fosters the social trust of workers.

HPC Resources of the Higher School of Economics

Abstract: The National Research University Higher School of Economics launched its HPC cluster and created a new division named the Supercomputer Simulation Unit. Now the university HPC cluster occupies seventh place in rating the most powerful computers of the CIS TOP50. The HPC cluster uses to solve machine learning problems, population genomics, hydrodynamics, atomistic and continuous modeling in physics, generative probabilistic models, financial row forecasting algorithms, and other actual problems. Paper describes the HSE HPC resources and experience of their use for scientific and educational tasks.

Membranes and Sheaves

Abstract: Our goal in this paper is to discuss a conjectural correspondence between the enumerative geometry of curves in Calabi–Yau 5-folds Z and 1-dimensional sheaves on 3-folds X that are embedded in Z as fixed points of certain C×-actions. In both cases, the enumerative information is taken in equivariant K-theory, where the equivariance is with respect to all automorphisms of the problem. In Donaldson–Thomas theory, one sums over all Euler characteristics with a weight (−q)χ, where q is a parameter, informally referred to as the boxcounting parameter. The main feature of the correspondence is that the 3-dimensional boxcounting parameter q becomes in dimension 5 the equivariant parameter for the C×-action that defines X inside Z. The 5-dimensional theory effectively sums up the q-expansion in the Donaldson–Thomas theory. In particular, it gives a natural explanation of the rationality (in q) of the DT partition functions. Other expected as well as unexpected symmetries of the DT counts follow naturally from the 5-dimensional perspective. These involve choosing different C×-actions on the same Z, and thus relating the same 5-dimensional theory to different DT problems. The important special case Z = X×C2 is considered in detail in Sections 7 and 8. If X is a toric Calabi–Yau 3-fold, we compute the theory in terms of a certain index vertex. We show that the refined vertex found combinatorially by Iqbal, Kozcaz, and Vafa is a special case of the index vertex. 1. A brief introduction 1.1 Overview Our goal in this paper is to discuss a conjectural correspondence between the enumerative geometry of curves in Calabi–Yau 5-folds Z and 1-dimensional sheaves on 3-folds X that are embedded in Z as fixed points of certain C×-actions. In both cases, the enumerative information is taken in equivariantK-theory, where the equivariance is with respect to all automorphisms of the problem. In Donaldson–Thomas theory, one sums over all Euler characteristics with weight (−q)χ, where q is a parameter. (Note the difference with the traditional weighing by qχ as in [MNOP06]. The change of sign of q fits much better with all correspondences.) Informally, q is referred to as the boxcounting parameter. The main feature of the correspondence is that the 3-dimensional boxcounting parameter q becomes in dimension 5 the equivariant parameter for the C×-action Received 15 April 2014, accepted in final form 9 October 2015. 2010 Mathematics Subject Classification 14N35.