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News
August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
Researchers from HSE MIEM and Samara University have developed the LRF-3D algorithm to automatically bypass idle nodes in three-dimensional networks-on-chip. Thanks to its hierarchical architecture, the algorithm outperforms existing solutions in both speed and path accuracy, improving processor reliability for use in data centres, supercomputers, and AI computing. The source code and test results are publicly available.
August 24, 2026
Researchers Develop Method for Direct Generation of Regulatory DNA
Researchers at HSE University have developed a model for generating promoters and enhancers—DNA sequences that regulate gene activity. The model works directly with DNA nucleotides, without first transforming them into a continuous numerical representation. This solution could be useful for applications in synthetic biology and gene therapy. The study results were presented at the ICLR 2026 Workshop ‘Generative AI in Genomics (Gen^2): Barriers and Frontiers.’
August 21, 2026
Social Integration: At the Crossroads of Knowledge and Values
The International Laboratory for Social Integration Research (ILSIR) at HSE University studies the challenges faced by vulnerable groups and explores ways to help them participate fully in everyday life. To develop effective solutions, the laboratory’s researchers combine cutting-edge methods with practical fieldwork. In this interview with the HSE News Service, Laboratory Head Elena Iarskaia-Smirnova discusses the laboratory’s work.

 

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Об одном подклассе решений уравнений редуцированной модели атмосферы

Вестник Московского университета. Серия 1: Математика. Механика. 2021. № 1. С. 24–29.
Turtsynskiy M.
Research target: Mathematics
Language: Russian
DOI
Keywords: дифференциальные уравненияособые точкимеханика сплошных сред
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Orbifold Saito theory of A and D type singularities
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Non-axiomatizability of modal predicate logics of Dedekind-complete linear orders with constant domains
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Semi-Interlaced Polytopes
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems. Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
A new spin on polynomial relations among kappa classes
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Any Topological Recursion on a Rational Spectral Curveis KP Integrable
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Сплетенный мир: кошка перевернулась. Доклад Римскому клубу
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Multiplicity-free products of Schubert divisors
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Mukai models of Fano varieties
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We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Mukai bundles on Fano threefolds
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We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Full exceptional collections on the symplectic isotropic Grassmannians
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Analog of theta-lifting for a curve over dual numbers over a finite field
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Quasi-periodic structures and "shrimps" in chaos on the example a two-mode van der Pol generator
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A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results.
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
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Added: August 29, 2026
Improving Differential Equation Solving in Compact Language Models via Activation Steering and Reinforcement Learning
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Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without ...
Added: July 8, 2026
Современные методы теории краевых задач. Понтрягинские чтения XXXVII.
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
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Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,  включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Comparative Study of Training Methods and Architectures of Echo State Networks
Androsov I., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3 P. 87–114
This paper examines echo state networks (ESNs), one of the most prevalent approaches to implementing reservoir computing. An ESN consists of a recurrent neural network with fixed (untrained) weights and a readout layer that is typically linear and trainable. This approach enables the creation of energyefficient and computationally efficient neural networks capable of real-time learning. However, since ...
Added: May 26, 2026
Об изоморфизме задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Решение дифференциальных уравнений с помощью языковых моделей из коробки: потенциал небольших LLM в математике
Koltsov S., Ignatenko V., Surkov A. et al., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 527 С. 311–319
В данной работе рассматривается способность малых рассуждающих языковых моделей к построению аналитических решений дифференциальных уравнений. Компьютерные эксперименты проводятся на таких моделях, как DeepSeek-R1-Distill-Qwen-1.5B, Qwen2.5-1.5B и Open-Reasoner-Zero-1.5B. Для извлечения финального ответа из рассуждений моделей используется постобработка на основе двух языковых моделей – Qwen2.5.latest и llama3.2.latest. Затем извлеченные ответы сравниваются с эталонными решениями с помощью метрики BLEU. ...
Added: November 27, 2025
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М.: ФГБУ «Российская академия наук», 2025.
СПЕЦИАЛЬНЫЙ ВЫПУСК: ТЕХНОЛОГИИ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА И МАШИННОГО ОБУЧЕНИЯ ...
Added: November 27, 2025
Transformers and State-Space Models: Fine-Tuning Techniques for Solving Differential Equations
Ignatenko V., Surkov A., Zakharov V. et al., Sci 2025 Vol. 7 No. 3 Article 130
Large language models (LLMs) have recently demonstrated remarkable capabilities in natural language processing, mathematical reasoning, and code generation. However, their potential for solving differential equations—fundamental to applied mathematics, physics, and engineering—remains insufficiently explored. For the first time, we applied LLMs as translators from the textual form of an equation into the textual representation of its ...
Added: October 10, 2025
Application of Large Language Models to Solving Differential Equations: Constructing Baseline Models with LSTM and GRU
Surkov A., Zakharov V., Sergei Koltcov et al., , in: Smart Technologies, Systems and Applications: 4th International Conference, SmartTech-IC 2024, Quito, Ecuador, December 2–4, 2024, Revised Selected Papers, Part IIVol. 2: Revised Selected Papers, Part II.: Springer, 2025. P. 239–252.
Currently, large language models are actively developing and beginning to be used to solve some mathematical problems. With the emergence of xLSTM model, which demonstrates the results comparable with transformer-based models, there has been a surge of interest in recurrent neural networks. This paper considers the application of baseline recurrent models such as LSTM and ...
Added: September 11, 2025
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В сборник включены статьи, раскрывающие возможные пути решения актуальных теоретических и практических проблем методики обучения математике в средней и высшей школе, различные направления модернизации отечественного математического образования и описывающие ряд актуальных результатов, полученных в различных областях математики. ...
Added: May 13, 2025
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