Китайско-российский студенческий математический семинар

Архив семинара

20 марта 2026 г.

1. Shan Jiang (Peking University, Beijing)
Quantum algorithms for matrix functions.

Аннотация

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/mAf9rFxRrDeU
Meeting code: 800-284-511
To join via a web browser: go to https://voovmeeting.com/; click "log In" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 800-284-511 in the "Enter meeting ID" field; when prompted, select "Join from browser".

Quantum algorithms have recently made significant progress in scientific computing, demonstrating their potential to overcome the limitations of classical computing power. In many scientific computing problems, including matrix inversion algorithms and Hamiltonian simulation, quantum algorithms have already demonstrated their quantum advantage within their frameworks. In this talk, we will first introduce some basic frameworks for applying quantum algorithms to scientific computing problems, and then present our recent work on matrix-valued functions based on Cauchy integrals and Fourier transforms.

2. V. I. Yashin (Steklov Mathematical Institute of Russian Academy of Sciences, Moscow)
Simulation of stabilizer quantum circuits and their reduction to classical Boolean circuits.

Аннотация

The talk will be streamed through “Kontur Talk”: https://mian.ktalk.ru/ojolwic9po4h?pinCode=5195.

Modern quantum computers suffer from noises, that is why a lot of effort is put in the theory of quantum error-correcting codes. Protocols of quantum fault-tolerance widely use a subclass of quantum computational processes called stabilizer circuits. Stabilizer circuits are most prone to error correction, they are capable of generating quantum entanglement, but they are also classically simulable. The general theory of stabilizer circuits and their classical simulation, in addition to practical significance to error-correction, turns out to have close connection with wide range of topics, such as: Boolean circuits, Boolean linear algebra, projective representations of abelian groups and their cohomology, linear optics, and theories of reference frames and hidden variable models from quantum foundations. In my talk, which is based on https://arxiv.org/abs/2511.05478, I will try to give an introduction to the subject and state some of my recent results.

06 марта 2026 г.

1. M. Ivlev, Novosibirsk State University
On commuting differential operators of rank 2 corresponding to trigonal spectral curves of genus 3.

Аннотация

The talk will be streamed through “Kontur Talk”: https://imsoran.ktalk.ru/ogsac0ijeetj.

Construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications to soliton theory. Operators of rank 1 in the case of smooth spectral curves were found by Krichever. The problem of constructing operators of rank $l > 1$ has not been solved in the general case. In all known examples of such operators, the spectral curves are hyperelliptic. In this report, the first examples of operators of rank 2 corresponding to trigonal spectral curves of genus 3 will be described.

2. Yuze Sun, Peking University, Beijing
Functoriality of coherent-constructible correspondence.

Аннотация

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/UqFOv8ai0tSh
Meeting code: 486-939-892
To join via a web browser: go to https://voovmeeting.com/; click "log In" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 486-939-892 in the "Enter meeting ID" field; when prompted, select "Join from browser".

In the context of homological mirror symmetry, the coherent-constructible correspondence (CCC) establishes a dictionary between the derived category of a toric variety and constructible sheaves, thus is a dictionary between algebraic and microlocal (reads as: symplectic geometry on a cotangent bundle) geometry.

We explore how algebraic geometric operations translate into microlocal ones. The talk will start from the basics of categorical knowledge, homological mirror symmetry and CCC. Then we will move to the functoriality of CCC, and possible extension to toric Artin stacks, based on Gaitsgory's (de-)equivariantization formalism.

19 декабря 2025 г.

1. She Yang, Peking University, Beijing
On the dynamical Mordell-Lang conjecture.

Аннотация

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/5xdJ4wc8cEUA
Number of the meeting: 908-331-123

The dynamical Mordell-Lang conjecture (DML) is one of the core problems in the field of arithmetic dynamics. It is the dynamical analogue of the Mordell-Lang conjecture (proved by Faltings-Vojta-McQuillan) in arithmetic geometry. The DML conjecture was formulated over a field of characteristic 0, but it is also natural to consider the same problem over fields of positive characteristic. In this talk, we will introduce some recent progress on the DML conjecture, with emphasis on the positive characteristic case.

2. Nikita Virin, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
An introduction to del Pezzo surfaces.

Аннотация

The talk will be streamed through "Kontur Talk": https://mian.ktalk.ru/kl37k35btugi?pinCode=3446

Del Pezzo surfaces form a class of varieties of great importance and interest in algebraic geometry. In this talk, we will discuss the basics on del Pezzo surfaces, including their classical and modern definitions. We will also discuss blow-up models of del Pezzo surfaces.

05 декабря 2025 г.

1. Dmitry Dudukalov (Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk)
Stochastic Dynamics Near Critical Points in Stochastic Gradient Descent.

Аннотация

Подключиться к докладу можно через "Kontur Talk": https://imsoran.ktalk.ru/ogsac0ijeetj

The talk will focus on limit theorems for stochastic gradient descent (SGD) and on how the choice of step size affects its convergence. We will begin by discussing the convergence of deterministic gradient descent with a constant step size, then review the classical Robbins–Monro result for SGD, and finally turn to several results from our joint work [1] concerning the convergence of SGD with a constant step size that tends to zero.

References:

D. Dudukalov, A. Logachov, V. Lotov, T. Prasolov, E. Prokopenko & A. Tarasenko, Convergence, Sticking and Escape: Stochastic Dynamics Near Critical Points in SGD, arXiv preprint, 2025, arXiv: 2505.18535

2. Zhangsong Li (Peking University, Beijing)
The Algorithmic Phase Transition for Correlated Spiked Models.

Аннотация

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/4TGPAsgr42lx.
Meeting code: 865-161-635
To join via a web browser: go to https://voovmeeting.com/; click "Log in" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 865-161-635 in the "Enter meeting ID" field; when prompted, select "Join from browser".

Modern multi-modal learning often relies on the premise that jointly analyzing multiple, related datasets can yield more powerful inferences than processing each one in isolation. We study this through the lens of a pair of spiked random matrices with correlated spikes. By proposing a novel subgraph counts algorithm, we show that the correlation between the spikes can be exploited for inference even in certain regimes where inference in each individual matrix is believed to be computationally intractable. Furthermore, we provide evidence for a matching computational lower bound based on the low-degree polynomial framework, suggesting our algorithm is optimal. Our results thus establish a new computational phase transition in correlated spiked models, delineating the boundary between what is efficiently possible and what is not. Based on arXiv:2511.06040.

21 ноября 2025 г.

1. Jianru Duan
Universal $L^2$-torsion detects fibered 3-manifolds.

Аннотация

It is well-known that the Alexander polynomial of a fibered knot must be monic. But in general the converse is not true. In this talk, we introduce the universal $L^2$-torsion of a 3-manifold, an invariant defined in analogy with the classical torsion, but using tools from $L^2$-theory. We will show that this invariant detects fibered 3-manifolds. Moreover, we extend the definition of the universal $L^2$-torsion to taut sutured 3-manifolds and show that it detects product sutured manifolds.

The talk will be streamed through "VooV": https://voovmeeting.com/r/374-057-208. To join via a web browser: go to https://voovmeeting.com/; click "Log in" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 374-057-208 in the "Enter meeting ID" field; when prompted, select "Join from browser".

2. Vasilii Rozhdestvenskii (Steklov Mathematical Institute of RAS)
The Steenrod problem on realization of cycles: old and new.

Аннотация

Singular homology groups form a basic invariant of a space, which allows to study its topological properties. Although they can be defined axiomatically, it is also useful (and quite agreeable) to think about them geometrically. In the late 1940s Steenrod asked whether a homology class can be represented by a continuous image of a fundamental class of a manifold. In the talk I will give an overview of results on this problem, presenting both classical and new ones.

Ссылка на трансляцию: https://mian.ktalk.ru/vhv429hulose?pinCode=9604