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Working paper

The description of global deformations of Lie algebras is important since it is related to unsolved problem of the classification of simple Lie algebras over a field of small characteristic.
In this paper we study global deformations of Lie algebras of type ${D}_{l}$ over an algebraically closed field K of characteristic 2. It is proved that Lie algebras of type $\bar{D_{l}}$
are rigid for odd $l>3$. Some global deformations of Lie algebras of type ${D}_{l}$ are constructed for even $l\ge 4$.

Added: Dec 8, 2017

Working paper

We study the connection between the affine degenerate Grassmannians in type $A$, quiver Grassmannians for one vertex loop quivers and affine
Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type $GL_n$ and identify it
with semi-infinite orbit closure of type $A_{2n-1}$. We show that principal quiver Grassmannians for the one vertex loop quiver
provide finite-dimensional approximations of the degenerate affine Grassmannian. Finally, we give an explicit
description of the degenerate affine Grassmannian of type $A_1^{(1)}$, propose
a conjectural description in the symplectic case and discuss the generalization to the case of the affine degenerate flag varieties.

Added: Oct 6, 2014

Working paper

Added: Feb 6, 2013

Working paper

Let M be a hyperkaehler manifold, and η a closed, positive (1,1)-form which is degenerate everywhere on M. We associate to η a family of complex structures on M, called a degenerate twistor family, and parametrized by a complex line. When η is a pullback of a Kaehler form under a Lagrangian fibration L, all the fibers of degenerate twistor family also admit a Lagrangian fibration, with the fibers isomorphic to that of L. Degenerate twistor families can be obtained by taking limits of twistor families, as one of the Kahler forms in the hyperkahler triple goes to η.

Added: Dec 27, 2013

Working paper

The article examines the role of degeneration theory in Russian medical and public discourses at the turn of the 20th century. Drawing on a wide range of historiography and primary sources, including archival records and medical writings, the article aims to outline different contexts of the concept’s usages: from rhetorical idioms to “scientific”, clinical and instrumental applications. Then, it seeks how psychiatrists defined the category of “socially dangerous” and tried to modify the existed institutional and legal framework. This focus could explain degeneration theory influence on social policy and the late imperial institutional system.

Added: Jan 18, 2017

Working paper

We study degenerations of Bethe subalgebras $B(C)$ in the Yangian $Y(\fgl_n)$, where $C$ is a regular diagonal matrix. We show that closure of the parameter space of the family of Bethe subalgebras is the Deligne-Mumford moduli space of stable rational curves $\overline{M_{0,n+2}}$ and state a conjecture generalizing this result to Bethe subalgebras in Yangians of arbitrary simple Lie algebra. We prove that all subalgebras corresponding to the points of $\overline{M_{0,n+2}}$ are free and maximal commutative. We also describe explicitly the ``simplest'' degenerations and show that every degeneration is the composition of the simplest ones.

Added: Mar 15, 2017

Working paper

We obtain several structure results for a class of spherical subgroups of connected reductive complex algebraic groups that extends the class of strongly solvable spherical subgroups. Based on these results, we construct certain one-parameter degenerations of the Lie algebras corresponding to such subgroups. As an application, we exhibit an explicit algorithm for computing the set of spherical roots of such a spherical subgroup.

Added: Jun 1, 2019

Working paper

Given a singular variety I discuss the relations between quantum cohomology of its resolution and smoothing. In particular, I explain how toric degenerations helps with computing Gromov--Witten invariants, and the role of this story in Fanosearch programme. The challenge is to formulate enumerative symplectic geometry of complex 3-folds in a way suitable for extracting invariants under blowups, contractions, and transitions.

Added: Sep 25, 2018

Working paper

The main goal of the present paper are new formulae for degrees of strata in Hurwitz spaces of rational functions having two degenerate critical values with preimages of prescribed multiplicities. We consider the case where the multiplicities of the preimages of one critical value are arbitrary, while the second critical value has degeneracy of codimension 1. Our formulae are based on the universal cohomological expressions for codimension 1 strata in terms of certain basic cohomology classes in general Hurwitz spaces of rational functions obtained by M. Kazarian and S. Lando. We prove new relations valid in cohomology of Hurwitz spaces that were conjectured by M. Kazarian on the base of computer experiments. As a corollary, we obtain new, previously unknown, explicit formulae for certain families of double Hurwitz numbers in genus 0. One may hope that the methods developed in the present paper are applicable to proving more general relations in cohomology rings of Hurwitz spaces and deducing more general formulae for double Hurwitz numbers.

Added: Nov 8, 2016

Working paper

I prove new local inequality for divisors on smooth surfaces, describe its applications, and compare it to a similar local inequality that is already known by experts.

Added: Dec 27, 2013

Working paper

Let X be a del Pezzo surface of degree 2 or greater over a finite field 𝔽_q. The image Γ of the Galois group Gal(\bar{𝔽}_q / 𝔽_q) in the group Aut(Pic(\bar{X})) is a cyclic subgroup preserving the anticanonical class and the intersection form. The conjugacy class of Γ in the subgroup of Aut(Pic(\bar{X})) preserving the anticanonical class and the intersection form is a natural invariant of X. We say that the conjugacy class of Γ in Aut(Pic(\bar{X})) is the type of a del Pezzo surface. In this paper we study which types of del Pezzo surfaces of degree 2 or greater can be realized for given q. We collect known results about this problem and fill the gaps.

Added: Dec 2, 2018

Working paper

We estimate δ-invariants of some singular del Pezzo surfaces with quotient singularities, which we studied ten years ago. As a result, we show that each of these surfaces admits an orbifold K\"ahler--Einstein metric.

Added: Oct 21, 2018

Working paper

We prove that δ-invariants of smooth cubic surfaces are at least 6/5.

Added: Dec 3, 2018

Working paper

This paper studies the behavior patterns among the theatre’s attendants in the process of ticket’s purchase. Since the theatre attempts to balance between the high rate of occupancy and the affordable prices for the spectator, the purpose of the study is to reveal the effects of changes in prices on attendance rate on different levels of attendance. This project is conducted conjointly with the Perm Tchaikovsky Opera and Ballet Theater. Data is taken from the sales information system of the theater for four seasons 2011-2012/2014-2015. The data is disaggregated to the level of the seating area and performance and consists of the attendance rate, the set of prices and the performance characteristics. The research explores the determinants of demand using censored quantile regression that accounts for the heterogeneity of effects on different levels of attendance rates and censoring. We have estimated the parameters of demand function and revealed that the aggregated demand is elastic by price, at the same time the elasticity varies across different seating areas. Moreover, demand for the more popular seats and performances expectedly turns out to be the less elastic.

Added: Jun 13, 2016

Working paper

This paper studies behavior patterns among theater attendees in the process of ticket purchasing. Since the theater attempts to balance between a high occupancy and affordable prices, the purpose of the study is to reveal the effects of changes in prices on attendance. This project is conducted conjointly with the Perm Tchaikovsky Opera and Ballet Theater. Data are taken from the sales information system of the theater for four seasons 2011-2012/2014-2015. The data are disaggregated to the level of the seating area and performance and consist of the attendance rate, the set of prices and the performance characteristics. The research explores the determinants of demand using a censored quantile regression which accounts for the heterogeneity of effects on different levels of attendance rates and censoring. We estimate the parameters of the demand function and show that the aggregated demand is elastic by price, at the same time the elasticity varies across different seating areas. Moreover, demand for the more popular seats and performances is less elastic

Added: Dec 5, 2016

Working paper

The article analyzes the role of the aristocracy in democratic Athens, i.e. in the Vth Century B.C. What happened to the aristocracy in democratic Athens? Whether the aristocrats were able to adapt themselves to new social and political realities? It is suggested that there took place their division into democratic and aristocratic politicians, a separation of democratically-oriented leaders (prostates tou demou), who managed to adapt to democratic institutions. The political actions of prostatai had features of demagogy. Thus we can assume that such a phenomenon as demagogy appeared much earlier than previously thought. The other part of aristocracy was not alien to demagogy as well. Suffice it to mention the efforts made by Thucydides son of Melesias, who created a political hybrid, of an aristocratic hetaireia which did not shun demagogic techniques

Added: Jun 22, 2015

Working paper

This study explores association between political regime, good governance and country social
performance measured as Infant Mortality Rate (IMR). It is widely argued that democratic leaders
possess more incentives to provide public goods, say, in order to meet median voter’s demands, than
their authoritarian counterparts, which, inter alia, leads to superior health related capabilities in democracies. Maintaining an assumption that in the modern world public health delivery process may
be of greater importance for certain health outcomes than macroeconomic and political factors, say,
economic growth, and capitalizing on the observation that an increasing number of nondemocratic
regimes perform well on governance and health indicators, whereas many democracies, especially
nascent, fare poorly, I argue that it is good governance that matters more for state performance in the
healthcare sector than democracy vs. autocracy dichotomy. Utilizing both cross-section and TSCS
data analysis, I show that good governance exerts systematic influence upon IMR, whereas political
regime characteristics lose their statistical significance once controlled for governance.

Added: Jan 30, 2014

Working paper

We propose a simple quality-ladder model with heterogeneous agents differing in their skills and wealth endowment to explain the persistence of barriers to entry in new democracies. In the model agents vote for a rate of redistribution and for the level of barriers to entry, which protect the incumbent firms from competition with new entrants. We show that even if a society democratizes, under certain conditions this leads only to the rise of redistribution, rather than to the elimination of barriers to entry. We show that this argument is particularly relevant for countries with a low level of human capital and high inequality in incomes and in skills.

Added: Feb 3, 2015

Working paper

Ballet S.,

math. arxive. Cornell University, 2017
We obtain new uniform bounds for the symmetric tensor rank of multiplication in finite extensions of any finite field Fp or Fp2 where p denotes a prime number greater or equal than 5. In this aim, we use the symmetric Chudnovsky-type generalized algorithm applied on sufficiently dense families of modular curves defined over Fp2 attaining the Drinfeld-Vladuts bound and on the descent of these families to the definition field Fp. These families are obtained thanks to prime number density theorems of type Hoheisel, in particular a result due to Dudek (2016).

Added: Jul 11, 2017

Working paper

The paper is dedicated to organizational dependence – independence of social enterprises (SEs) taking into account their multifaceted nature and complex business models shaping in line with the task of solving social problems at the crossroads of market, not-for-profit activity and state regulation. The paper is aimed at theoretical and empirical clarification of organizational nature of SEs on the basis of the international comparative study. We aimed to clarify the following issues: - To what extent the SEs in different countries (macro-regions) are oriented to the distinct forms of partnerships and do any of them have special bias to the state? - What factors play the main role in the character of a SE partnership (interactions) with stakeholders? - Do partnership forms relate to the level of independence of a SE from some bigger organizations or from the state? - Can we say that “independence” is most likely a characteristics of predominantly market oriented SEs (in terms of business model choice)? As the sampling frame of the survey we used the database of the fellows of Ashoka International network — the largest organization supported the leaders of social entrepreneurship worldwide. Respondents filled online a formalized questionnaire with 76 questions, and for the period from May through November, 2012 we received 128 questionnaires from 38 countries worldwide filled in English or Spanish. The subject of the research is social and economic activity of the SEs including strategy formation, assessment of condition of the target social groups, fundraising, partnership with other organizations, interactions with local and central governments, social, economic and institutional barriers of organizational activity. The data were processed with a SPSS package.

Added: Mar 29, 2015

Working paper

The paper is dedicated to organizational dependence – independence of social enterprises (SEs) taking into account their multifaceted nature and complex business models shaping in line with the task of solving social problems at the crossroads of market, not-for-profit activity and state regulation

Added: Dec 3, 2013