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September 25, 2026
AI Users Earn Up to 41.8% More Than Non-Users
Research conducted by economists at HSE University has revealed a significant correlation between the regular use of GenAI in the workplace and higher pay among Russian employees. The study found that individuals who frequently use GenAI in their professional activities earn notably more than those who reject these new tools or resort to them occasionally. The salary premium for highly qualified specialists reaches 41.8%. The article was published in the Voprosy Ekonomiki journal.
September 24, 2026
‘Feedback and Constructive Criticism Are Essential in Our Profession
Vincent Fardeau, Associate Professor at HSE ICEF, has reached a major career milestone: he recently published his paper ‘Asymmetric Thin Markets’ in the Journal of Financial Economics, successfully passed his major academic review, and received tenure. In this interview, Vincent discusses the story behind the paper, explains the concept of asymmetric thin markets, and shares his advice for young scholars aiming to publish in top-tier journals.
September 22, 2026
Personal Interest in Doctoral Thesis Topic Most Important for Confidence in Successful Defence
A researcher at HSE University analysed data on 1,539 doctoral students from 161 Russian universities to identify which features of a thesis topic are associated with academic success and engagement. The most important factor was found to be personal interest in the research topic, which was associated with almost all key aspects of doctoral programme experience—from engaging with the academic supervisor to research activity and confidence about successfully defending the thesis. The findings have been published in Higher Education.

 

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Surveys in Differential Geometry. Volume 24 (2019).

Vol. 24: Differential geometry, Calabi-Yau theory, and general relativity. International Press of Boston Inc, 2019.
Under the general editorship: H. Cao, S. Yau
Chapters
Conformally maximal metrics for Laplace eigenvalues on surfaces
Penskoi A., Karpukhin M., Polterovich I. et al., , in: Surveys in Differential Geometry. Volume 24 (2019).Vol. 24: Differential geometry, Calabi-Yau theory, and general relativity.: International Press of Boston Inc, 2019.
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili–Sire and Petrides using related, though different methods. In particular, it was shown that for a given , the maximum of ...
Added: January 31, 2025
Language: English
Keywords: дифференциальная геометрия Differential Geometry
Surveys in Differential Geometry. Volume 24 (2019).
Similar publications
Upper bounds for Steklov eigenvalues of a hypersurface of revolution
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
On the rigidity of complex Hirzebruch genera on SU-manifolds
Черных Г. С., European Journal of Mathematics 2025 No. 11 Article 27
We prove that if a complex genus ϕ : U → R is rigid on SU-manifolds with a torus action then ϕ is the elliptic Krichever genus. ...
Added: August 29, 2025
Conformally maximal metrics for Laplace eigenvalues on surfaces
Penskoi A., Karpukhin M., Polterovich I. et al., , in: Surveys in Differential Geometry. Volume 24 (2019).Vol. 24: Differential geometry, Calabi-Yau theory, and general relativity.: International Press of Boston Inc, 2019.
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this problem has been recently achieved by Nadirashvili–Sire and Petrides using related, though different methods. In particular, it was shown that for a given , the maximum of ...
Added: January 31, 2025
Canonical curves and Kropina metrics in Lagrangian contact geometry
Ma Tianyu, Flood K. J., Matveev V. et al., Nonlinearity 2024 Vol. 37 No. 1 Article 015007
We present a Fefferman-type construction from Lagrangian contact to split-signature conformal structures and examine several related topics. In particular, we describe the canonical curves and their correspondence. We show that chains and null-chains of an integrable Lagrangian contact structure are the projections of null-geodesics of the Fefferman space. Employing the Fermat principle, we realize chains ...
Added: March 6, 2024
Statistical field theory of mechanical stresses in Coulomb fluids: general covariant approach vs Noether’s theorem
Petr E Brandyshev, Yury A Budkov, Journal of Statistical Mechanics: Theory and Experiment 2023 No. 12 Article 123206
In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether's first theorem for the case of a fluctuating order parameter to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and fluctuation corrections derived ...
Added: December 18, 2023
Noether’s second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids
Brandyshev P., Budkov Y., Journal of Chemical Physics 2023 Vol. 158 No. 17 Article 174114
In this paper, we present a covariant approach that utilizes Noether’s second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach ...
Added: May 5, 2023
Мультипликативный интеграл и его приложения в дифференциальной геометрии
Петрова В., Дмитриева М., Сивиркина А., LAP LAMBERT Academic Publishing, 2018.
Как известно, риманов интеграл это предел интегральной суммы. В определении мультипликативного интеграла речь идет о пределе произведения большого числа сомножителей, близких к единице - алгебраической операции, вообще говоря, не коммутативной. Теорию мультипликативного интеграла естественно рассматривать, как более общую, чем теория риманова интеграла. Ее специфика проистекает именно из некоммутативности умножения. Понятие мультипликативного интеграла ввел Вольтерра в ...
Added: December 2, 2019
Bounds on Multiplicities of Laplace-Beltrami Operator Eigenvalues on the Real Projective Plane
Penskoi A., Nadirashvili N., Berdnikov A., / Series arXiv "math". 2016.
The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bounds for Dirichlet, Neumann and Steklov eigenvalues on the real projective plane with holes are also provided. ...
Added: March 21, 2017
Compact fibrations with hyperk ̈ahler fibers
Déev R. N., / Series arXiv "math". 2016.
Essential dimension of a family of complex manifolds is the dimension of the image of its base in the Kuranishi space of the fiber. We prove that any family of hyperk\"ahler manifolds over a compact simply connected base has essential dimension not greater than 1. A similar result about families of complex tori is also ...
Added: September 23, 2016
Absolutely trianalytic tori in the generalized Kummer variety
Kurnosov N., / Series math "arxiv.org". 2015.
We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori. ...
Added: October 16, 2015
Higher Trace and Berezinian of Matrices over a Clifford Algebra
Covolo T., Ovsienko V., Poncin N., Journal of Geometry and Physics 2012 Vol. 62 P. 2294–2319
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n graded commutative associative algebra. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonn\'e determinant of quaternionic ...
Added: September 28, 2015
Full symplectic packing for tori and hyperkahler manifolds
Entov M., Verbitsky M., / Series math "arxiv.org". 2014.
Let M be a closed symplectic manifold of volume V. We say that M admits a full symplectic packing by balls if any collection of symplectic balls of total volume less than V admits a symplectic embedding to M. In 1994 McDuff and Polterovich proved that symplectic packings of Kahler manifolds can be characterized in ...
Added: February 5, 2015
Dynamic alpha-invariants of del Pezzo surfaces
Ivan Cheltsov, Martinez-Garcia J., / Series math "arxiv.org". 2014.
For every smooth del Pezzo surface $S$, smooth curve $C\in|-K_{S}|$ and $\beta\in(0,1]$, we compute the $\alpha$-invariant of Tian $\alpha(S,(1-\beta)C)$ and prove the existence of K\"ahler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2\pi\beta$ for $\beta$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as ...
Added: February 5, 2015
Existence of HKT metrics on hypercomplex manifolds of real dimension 8
Verbitsky M., Grantcharov G., Lejmi M., / Series math "arxiv.org". 2014.
A hypercomplex manifold M is a manifold equipped with three complex structures satisfying quaternionic relations. Such a manifold admits a canonical torsion-free connection preserving the quaternion action, called Obata connection. A quaternionic Hermitian metric is a Riemannian metric on which is invariant with respect to unitary quaternions. Such a metric is called HKT if it ...
Added: September 19, 2014
Morrison-Kawamata cone conjecture for hyperkahler manifolds
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Let $M$ be a simple holomorphically symplectic manifold, that is, a simply connected holomorphically symplectic manifold of Kahler type with $h^{2,0}=1$. We prove that the group of holomorphic automorphisms of $M$ acts on the set of faces of its Kahler cone with finitely many orbits. This is a version of the Morrison-Kawamata cone conjecture for ...
Added: September 5, 2014
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