Algebra, Geometry, and AI: Russian and Vietnamese Mathematicians Discuss Current Research

© HSE University

A delegation of scientists from Hanoi visited the HSE Faculty of Computer Science and then took part in a Russian-Vietnamese conference in St Petersburg. The events were part of the three-year project ‘Flexibility and Computational Methods.’ Over the course of the project, the researchers have prepared joint publications and obtained new mathematical results.

In August 2026, scientists from the HSE Faculty of Computer Science and the Institute of Mathematics of the Vietnam Academy of Science and Technology held two joint academic events—a seminar in Moscow and a conference in St Petersburg. The meetings took place as part of the ‘Flexibility and Computational Methods’ project. The participants discussed current problems in algebraic geometry and commutative algebra, presented their research findings, and identified areas for further cooperation.

Moscow Meeting: New Problems and Shared Research Interests

The Russian-Vietnamese Seminar on Algebraic Geometry and Commutative Algebra was held at the HSE Faculty of Computer Science from August 19 to 21, 2026. The delegation of scientists from Hanoi was led by Ngo Viet Trung, a full member of the Vietnam Academy of Science and Technology (VAST), President of the Vietnam Mathematical Society and Chief Research Fellow at the VAST Institute of Mathematics. The delegation also included Professors Do Trong Hoang, Nguyen Bich Van, and Nguyen Thi Thanh Tam.

Scientists from both sides delivered several lectures, including some for early-career researchers. The seminar provided an opportunity for the Vietnamese colleagues to learn more about HSE University and to exchange experience in teaching and research. Vietnamese students showed great interest in the lectures delivered by researchers from the Laboratory on Algebraic Transformation Groups.

Lectures by Vietnamese and Russian Scientists

1. Asymptotic Behaviour of Saturation Degree, Ngo Viet Trung

2. Asymptotic Regularity and Depth of Invariant Chains of Edge Ideals, Do Trong Hoang

3. The Jung–Van Der Kulk Theorem, Anton Shafarevich

4. Additive Actions and Gorenstein Algebras, Yulia Zaitseva

Anton Shafarevich

‘We designed the programme to combine presentations of our new results with discussions of classical topics. The main goal was simple—to learn more about each other’s research interests and find new areas of overlap. At the HSE Faculty of Computer Science, I gave a talk on the classical Jung–van der Kulk theorem on automorphisms of the affine plane. This is one of the key results in affine algebraic geometry, and there are many proofs of it. I chose one based on the properties of algebraic group actions on varieties. This is a method that our laboratory is particularly familiar with, and I wanted to demonstrate clearly how it works,’ said Anton Shafarevich, Senior Research Fellow at the HSE Laboratory on Algebraic Transformation Groups.

Five-Day Discussions in St Petersburg

The Russia-Vietnam Conference on Algebraic Geometry, Algebraic Groups, Commutative Algebra, and Applications was held at the Leonhard Euler International Mathematical Institute from August 24 to 28, 2026. In St Petersburg, the delegation was joined by Professor Hoang Le Truong, head of the Vietnamese project team, who is known for his work in algebraic geometry and for developing software for computational experiments.

Over five days, the participants discussed a wide range of topics—from the regularity functions of powers of graded ideals to the flexibility of spherical varieties and the use of large language models for automated theorem proving.

Ivan Arzhantsev

‘Our research interests and the research conducted at the VAST Institute of Mathematics complement each other very well, allowing each research group to strengthen its expertise. The presentations by the HSE University project participants focused on the structural theory of algebraic groups and the theory of algebraic transformation groups, while each of our Vietnamese colleagues gave a detailed presentation of their recent research findings. I would also like to highlight the involvement of mathematicians from St Petersburg, who delivered excellent presentations and actively participated in the discussions,’ said Ivan Arzhantsev, Dean of the HSE Faculty of Computer Science and Head of the Laboratory on Algebraic Transformation Groups.

He expressed his gratitude to the Leonhard Euler International Mathematical Institute for its hospitality and support in organising the conference. ‘We hope that our application to continue the joint project with the VAST Institute of Mathematics in Hanoi for another three years will receive support under the International Academic Cooperation of HSE University programme, allowing us to continue developing productive cooperation with Vietnamese mathematicians,’ he stressed.

Conference Topics and Speakers

1. Generators of Linear Algebraic Groups, Ivan Arzhantsev
2. Polar Cylinders and Ga-Actions on Affine Cones of Cubic Fourfolds Containing a Plane, Hoang Le Truong
3. Regularity Functions of Powers of Graded Ideals, Ngo Viet Trung
4. On the Generalised Bass-Quillen Conjecture in Dimension 2, Anastasia Stavrova
5. Induced and Restricted Representations of Kumjian–Pask Algebras of Higher-Rank Graphs, Nguyen Bich Van
6. Root Monoids, Yulia Zaitseva
7. Flat Surfaces in Three Homogeneous Spaces, Belarbi Lakehal
8. Homological Invariants of Ideals Associated with Ferrers Diagrams, Do Trong Hoang
9. Chow Motives of Some Mukai Variety, Viktor Petrov
10. On the Regular Borel Subalgebras of the Lie Algebra of Aut(A^2), Ananya Pal
11. Flexibility of Spherical Varieties, Anton Shafarevich
12. Flexibility of Affine Horospherical Varieties, Veronika Kikteva
13. On Flexibility of Affine Factorial Varieties, Kirill Shakhmatov
14. Nilpotency of Locally Isotropic K_1 Functor, Egor Voronetsky
15. Additive Actions on Projective Surfaces with Finitely Many Orbits, Alexander Perepechko
16. Tangent Cones to Schubert Varieties for Affine Kac–Moody Groups and Embeddings of Weyl Groups, Mikhail Ignatev
17. Normalisers of Certain Subgroups of a Chevalley Group over a Ring, Alexei Stepanov
18. Flexibility and the Cox Construction, Sergey Gayfullin
19. Explicit Formulas for the Depth Function of Cover Ideals of Path Graphs, Nguyen Thi Thanh Tam
20. A Survey of Large Language Models in Automated Theorem Proving / GammaZero: Hierarchical Search for Automated Theorem Proving, Dang Van Khai, Nguyen Duc Huy
21. Additive Actions on Degenerate Projective Hypersurfaces, Ivan Beldiev

‘Finding New Areas of Overlap’

The full member of the Vietnam Academy of Science and Technology (VAST), Ngo Viet Trung, highlighted the practical value of the Moscow seminar and St Petersburg conference for developing future joint research.

Ngo Viet Trung

‘The seminar at HSE University and the conference in St Petersburg were very useful for us. From the presentations by our Russian colleagues, we learned about new problems in both algebra and geometry that could eventually serve as a basis for joint research projects between Professor Ivan Arzhantsev’s research group and research groups working in algebra and geometry in Hanoi. We were very impressed by the reputation and infrastructure of HSE University, which represents a new model of education in Russia. We also had the opportunity to visit many interesting places in Moscow and St Petersburg. We were all impressed by the Russian people and culture. This trip will remain an unforgettable experience for us,’ said Ngo Viet Trung.

Hoang Le Truong, head of the Vietnamese team of the ‘Flexibility and Computational Methods’ project, also praised both the academic and personal aspects of the trip.

Hoang Le Truong

‘My trip to Russia was truly remarkable and, in many ways, opened up new horizons for me. To be honest, before arriving, I did not have a clear idea of what to expect, but the experience exceeded all my expectations and was full of pleasant surprises—from the warm hospitality of our hosts to the vibrant and stimulating intellectual atmosphere,’ he said.

Hoang Le Truong also mentioned that the conference had made a particularly strong impression on him. ‘It was incredibly dynamic and genuinely intense—not only because of the topics being discussed, but also because of the energy in the room. There were many fascinating presentations on the most up-to-date research, and I was particularly impressed by the large number of early-career researchers presenting work of a genuinely high standard. Their confidence, creativity, and rigorous methodology deserve special attention and made the discussions even more substantive and engaging. It was not only a productive academic event, but also a memorable and enriching experience, particularly in terms of discovering the history, culture, and people of Russia,’ Hoang Le Truong said.

Each research school has its own strengths, Anton Shafarevich noted. ‘We specialise in the theory of algebraic transformation groups, while our Vietnamese colleagues are experts in commutative algebra. At meetings like these, we can compare approaches, learn from one another, and see where our methods complement each other,’ he explained.

Anastasia Stavrova

Anastasia Stavrova, Senior Research Fellow at the St Petersburg Branch of the Steklov Mathematical Institute of the Russian Academy of Sciences and an invited speaker at the International Congress of Mathematicians 2026, also highlighted the atmosphere of the academic event. ‘I remember the conference for its very friendly and welcoming atmosphere. Our Vietnamese colleagues are highly accomplished specialists. In particular, their presentations on the use of artificial intelligence in mathematics attracted a great deal of interest,’ she said.

From Joint Publications to New Mathematical Results

The seminar and conference were held as part of the concluding three-year joint project ‘Flexibility and Computational Methods’ under the International Academic Cooperation of HSE University programme. The project is being carried out in 2024–2026 by the Laboratory on Algebraic Transformation Groups at the HSE Faculty of Computer Science and a research team from the Institute of Mathematics of the Vietnam Academy of Science and Technology.

During the project, the researchers have produced numerous publications, including joint papers, and solved a number of important problems. In particular, they proved the flexibility of the affine cone over the intersection of two quadrics—a result by Kirill Shakhmatov and Hoang Le Truong—and the flexibility of any non-degenerate affine spherical variety—a result by Anton Shafarevich.

The project received a positive assessment from the Russian-Vietnamese Intergovernmental Commission. In 2025, it was officially recognised as part of the Sixth Meeting of the Russian-Vietnamese Commission on Education, Science, and Technology Cooperation.

The St Petersburg Russian-Vietnamese conference was included in the Year of Russian-Vietnamese Cooperation in Science and Education. It was the second conference in a series of joint meetings held as part of the ‘Flexibility and Computational Methods’ project. The first conference took place in Hanoi in May 2025.

The project participants hope to continue their cooperation and develop joint research in algebra and algebraic geometry.