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 & Computer science. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

Pursuing the double affine Grassmannian, I: Transversal slices via instantons on $A_k$-singularities

Abstract: This article is the first in a series that describes a conjectural analog of the geometric Satake isomorphism for an affine Kac-Moody group. (For simplicity, we only consider the untwisted and simply connected case here.) The usual geometric Satake isomorphism for a reductive group G identifies the tensor category Rep(G∨) of finite-dimensional representations of the Langlands dual group G∨ with the tensor category PervG(O)(GrG) of G(O)-equivariant perverse sheaves on the affine Grassmannian GrG=G(K)/G(O) of G. (Here K=C((t)) and O=C[[t]].) As a by-product one gets a description of the irreducible G(O)-equivariant intersection cohomology (IC) sheaves of the closures of G(O)-orbits in GrG in terms of q-analogs of the weight multiplicity for finite-dimensional representations of G∨. The purpose of this article is to try to generalize the above results to the case when G is replaced by the corresponding affine Kac-Moody group Gaff. (We refer to the (not yet constructed) affine Grassmannian of Gaff as the double affine Grassmannian.) More precisely, in this article we construct certain varieties that should be thought of as transversal slices to various Gaff(O)-orbits inside the closure of another Gaff(O)-orbit in GrGaff. We present a conjecture that computes the intersection cohomology sheaf of these varieties in terms of the corresponding q-analog of the weight multiplicity for the Langlands dual affine group Gaff∨, and we check this conjecture in a number of cases. Some further constructions (such as convolution of the corresponding perverse sheaves, analog of the Beilinson-Drinfeld Grassmannian, and so forth) will be addressed in another publication

Gushel–Mukai varieties: Linear spaces and periods

Abstract: Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic 4-fold and the primitive second cohomology of its variety of lines, a smooth hyper-Kahler 4-fold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel–Mukai varieties of dimension 4 (resp., 6), that is, smooth dimensionally transverse intersections of the cone over the Grassmannian Gr(2,5), a quadric, and two hyperplanes (resp., of the cone over Gr(2,5) and a quadric). The associated hyper-Kahler 4-fold is in both cases a smooth double cover of a hypersurface in P5 called an Eisenbud–Popescu–Walter sextic.

Understanding Authoritarian Regionalism

Abstract: Anastassia V. Obydenkova is grateful to the Princeton Institute for International and Regional Studies (Princeton University) and to Harvard University’s Davis Center for Russian and Eurasian Studies for supporting her research presented in this article. Her research was cofunded by the Fung Global Fellows Program at the Princeton Institute for International and Regional Studies (PIIRS), Princeton University, and by the Niehaus Center for Globalization and Governance, Princeton University.

Economic Cycles, Crises, and the Global Periphery

Abstract: Introduction: cyclical and world-systemic aspects of economic reality with respect to contemporary crisis -- Kondratieff waves in the world system perspective -- Interaction between Kondratieff waves and juglar cycles -- From Kondratieff waves to Akamatsu waves? A new center-periphery perspective on long cycles -- Conclusion: new Kondratieff waves and forthcoming global social transformation .