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.

Mapping class group and a global Torelli theorem for hyperkähler manifolds

Abstract: A mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies. We compute a mapping class group of a hyperkahler manifold M, showing that it is commensurable to an arithmetic lattice in SO(3,b2−3). A Teichmuller space of M is a space of complex structures on M up to isotopies. We define a birational Teichmuller space by identifying certain points corresponding to bimeromorphically equivalent manifolds. We show that the period map gives the isomorphism between connected components of the birational Teichmuller space and the corresponding period space SO(b2−3,3)/SO(2)×SO(b2−3,1). We use this result to obtain a Torelli theorem identifying each connected component of the birational moduli space with a quotient of a period space by an arithmetic group. When M is a Hilbert scheme of n points on a K3 surface, with n−1 a prime power, our Torelli theorem implies the usual Hodge-theoretic birational Torelli theorem (for other examples of hyperkahler manifolds, the Hodge-theoretic Torelli theorem is known to be false).

A commutative algebra on degenerate CP1 and Macdonald polynomials

Abstract: We introduce a unital associative algebra A associated with degenerate CP1. We show that A is a commutative algebra and whose Poincare series is given by the number of partitions. Thereby, we can regard A as a smooth degeneration limit of the elliptic algebra introduced by Feigin and Odesskii [Int. Math. Res. Notices 11, 531 (1997)]. Then we study the commutative family of the Macdonald difference operators acting on the space of symmetric functions. A canonical basis is proposed for this family by using A and the Heisenberg representation of the commutative family studied by Shiraishi [ Commun. Math. Phys. 263, 439 (2006)]. It is found that the Ding–Iohara algebra [Lett. Math. Phys. 41, 183 (1997)] provides us with an algebraic framework for the free field construction. An elliptic deformation of our construction is discussed, showing connections with the Drinfeld quasi-Hopf twisting [Leningrad Math. J. 1, 1419 (1990)] in the sence of Babelon-Bernard–Billey [Phys. Lett. B. 375, 89 (1996)], the Ruijsenaar...

Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning

Abstract: Uncertainty estimation and ensembling methods go hand-in-hand. Uncertainty estimation is one of the main benchmarks for assessment of ensembling performance. At the same time, deep learning ensembles have provided state-of-the-art results in uncertainty estimation. In this work, we focus on in-domain uncertainty for image classification. We explore the standards for its quantification and point out pitfalls of existing metrics. Avoiding these pitfalls, we perform a broad study of different ensembling techniques. To provide more insight in the broad comparison, we introduce the deep ensemble equivalent (DEE) and show that many sophisticated ensembling techniques are equivalent to an ensemble of very few independently trained networks in terms of the test log-likelihood.