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.

Flops and spherical functors

Abstract: We study derived categories of Gorenstein varieties X and X^+ connected by a flop. We assume that the flopping contractions f: X \to Y, f^+: X^+ \to Y have fibers of dimension bounded by 1 and Y has canonical hypersurface singularities of multiplicity 2. We consider the fiber product W=X \times_Y X^+ with projections p: W \to X, q: W \to X^+ and prove that the flop functors F = Rq_* Lp^*: D^b(X) \to D^b(X^+), F^+= Rp_*Lq^*: D^b(X^+) \to D^b(X) are equivalences, inverse to those constructed by M. Van den Bergh. The composite F^+ \circ F: D^b(X) \to D^b(X) is a non-trivial auto-equivalence. When variety Y is affine, we present F^+\circ F as the spherical cotwist associated to a spherical functor \Psi. The functor \Psi is constructed by deriving the inclusion of the null-category A_f of sheaves F in \Coh (X) with Rf_*(F)=0 into Coh (X). We construct a spherical pair (D^b(X),D^b(X^+)) in the quotient D^b(W)/K^b, where K^b is the common kernel of the derived push-forwards for the projections to X and X^+, thus implementing in geometric terms a schober for the flop. A technical innovation of the paper is the L^1f^*f_* vanishing for the Van den Bergh's projective generator. We construct a projective generator in the null-category and prove that its endomorphism algebra is the contraction algebra.

Self-excited multifractal dynamics

Abstract: We introduce the self-excited multifractal (SEMF) model, defined such that the amplitudes of the increments of the process are expressed as exponentials of a long memory of past increments. The principal novel feature of the model lies in the self-excitation mechanism combined with exponential nonlinearity, i.e. the explicit dependence of future values of the process on past ones. The self-excitation captures the microscopic origin of the emergent endogenous self-organization properties, such as the energy cascade in turbulent flows, the triggering of aftershocks by previous earthquakes and the "reflexive" interactions of financial markets. The SEMF process has all the standard stylized facts found in financial time series, which are robust to the specification of the parameters and the shape of the memory kernel: multifractality, heavy tails of the distribution of increments with intermediate asymptotics, zero correlation of the signed increments and long-range correlation of the squared increments, the asymmetry (called "leverage" effect) of the correlation between increments and absolute value of the increments and statistical asymmetry under time reversal.

The Young Bouquet and Its Boundary

Abstract: The classification results for the extreme characters of two basic “big” groups, the infinite symmetric group S(∞) and the infinite-dimensional unitary group U(∞), are remarkably similar. It does not seem to be possible to explain this phenomenon using a suitable extension of the Schur–Weyl duality to infinite dimension. We suggest an explanation of a different nature that does not have analogs in the classical representation theory. We start from the combinatorial/probabilistic approach to characters of “big” groups initiated by Vershik and Kerov. In this approach, the space of extreme characters is viewed as a boundary of a certain infinite graph. In the cases of S(∞) and U(∞), those are the Young graph and the Gelfand–Tsetlin graph, respectively. We introduce a new related object that we call the Young bouquet. It is a poset with continuous grading whose boundary we define and compute. We show that this boundary is a cone over the boundary of the Young graph, and at the same time it is also a degeneration of the boundary of the Gelfand–Tsetlin graph. The Young bouquet has an application to constructing infinite-dimensional Markov processes with determinantal correlation functions.

Different Single-Photon Response of Wide and Narrow Superconducting Mo x Si 1 − x Strips

Abstract: The photon count rate (PCR) of superconducting single-photon detectors made of ${\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\text{\ensuremath{-}}x}$ films shaped as a 2-$\ensuremath{\mu}\mathrm{m}$-wide strip and a 115-nm-wide meander strip line is studied experimentally as a function of the dc biasing current at different values of the perpendicular magnetic field. For the wide strip, a crossover current ${I}_{\mathrm{cross}}$ is observed, below which the PCR increases with an increasing magnetic field and above which it decreases. This behavior contrasts with the narrow ${\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\text{\ensuremath{-}}x}$ meander, for which no crossover current is observed, thus suggesting different photon-detection mechanisms in the wide and narrow strips. Namely, we argue that in the wide strip the absorbed photon destroys superconductivity locally via the vortex-antivortex mechanism for the emergence of resistance, while in the narrow meander superconductivity is destroyed across the whole strip line, forming a hot belt. Accordingly, the different photon-detection mechanisms associated with vortices and the hot belt determine the qualitative difference in the dependence of the PCR on the magnetic field.