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Of all publications in the section: 3 536
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Working paper
Chebochko N.G. arxiv.org. math. Cornell University, 2017. No. 1712.01810.
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 $l\ge 4$.
Working paper
Feigin E., Finkelberg M. V., Reineke M. arxiv.org. math. Cornell University, 2014. No. 1410.0777.
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.
Working paper
Feigin E. arxiv.org. math. Cornell University, 2012
Working paper
Verbitsky M. arxiv.org. math. Cornell University, 2013
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.
Working paper
Pogorelov M. Humanities. HUM. Basic Research Programme, 2016. No. 139.
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.
Working paper
Aleksei Ilin, Leonid Rybnikov. Series math "arxiv.org". arXiv:1703.04147. Cornell University, 2017
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.
Working paper
Roman Avdeev. arxiv.org. math. Cornell University, 2019. No. 1905.01169.
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.
Working paper
Galkin S. arxiv.org. math. Cornell University, 2018. No. 1809.02737.
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.
Working paper
Bychkov B. Working papers by Cornell University. Cornell University, 2016
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.
Working paper
Ivan Cheltsov. arxiv.org. math. Cornell University, 2013
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.
Working paper
Trepalin A. math. arxive. Cornell University, 2018
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.
Working paper
Cheltsov I., Shramov K., Park J. arxiv.org. math. Cornell University, 2018
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.
Working paper
Cheltsov I., Zhang K. math. arxive. Cornell University, 2018
We prove that δ-invariants of smooth cubic surfaces are at least 6/5.
Working paper
Ozhegova A., Ozhegov E. M. Working papers. AWP. ACEI, 2016. No. 05 - 2016.
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.
Working paper
Ozhegov E. M., Ozhegova A. Economics/EC. WP BRP. Высшая школа экономики, 2016. No. WP BRP 156/EC/2016 .
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
Working paper
Gushchin V. Humanities. HUM. Basic Research Programme, 2015. No. WP BRP 101/HUM/2015 .
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
Working paper
Rosenberg D. Политическая теория и политический анализ. WP14. Высшая школа экономики, 2014. No. 01.
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.
Working paper
Veselov D. A. Documents de travail du Centre d'Economie de la Sorbonne. cesdoc:13050. Centre d'Economie de la Sorbonne, 2015
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.