G. Smirnov

activity

20102026

most citedTypes of critical points of the Kowalevski gyrostat in double field

3 citations · 9 across the 15 of their papers we have counts for

collaborators

17 papers

math.DS2026

First integrals of dense hard-ball gases

Gleb Smirnov

We answer two questions of Kozlov about polynomial-in-momentum first integrals of billiard systems. For billiards in bounded polytopes, such integrals are independent of position.…

math.DG2025

Anti-self-dual blowups II

Vsevolod Shevchishin, Gleb Smirnov

Let $X$ be a closed, oriented four-manifold with $b_{2}^{+} \leq 3$ , and suppose $X$ contains a collection of pairwise disjoint embedded $(- 2)$ -spheres. We prove that there is a Rieman…

math.DG2023

Anti-self-dual blowups

Vsevolod Shevchishin, Gleb Smirnov

Let $X$ be a closed, oriented four-manifold containing an embedded sphere with self-intersection number $(- 1)$ . Suppose that $b_{2}^{+} (X) \leq 3$ . We show that there exists a Riemanni…

math.SG2022

On Lagrangian tori in K3 surfaces

Gleb Smirnov

Every Maslov-zero Lagrangian torus in a K3 surface has non-trivial homology class. This note aims to extend this result to Lagrangian tori with Maslov indices congruent to zero mod…

math.SG2022

Symplectic mapping class groups of blowups of tori

Gleb Smirnov

Let $ω$ be a Kaehler form on the real $4$ -torus $T^{4}$ . Suppose that $ω$ satisfies an irrationality condition which can be achieved by an arbitrarily small perturbation of $ω$ . This…

math.SG2021

Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants

Gleb Smirnov

The purpose of this note is to prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated. Our proof makes no use of any Floer-theoretic machinery…

math.SG2020

Seidel's theorem via gauge theory

Gleb Smirnov

A new proof is given that Seidel's generalized Dehn twist is not symplectically isotopic to the idenity.

math.SG2020

Infinitely many non-isotopic real symplectic forms on $S^{2} \times S^{2}$

Gleb Smirnov

Let $(S^{2}, ω)$ be a symplectic sphere, and let $τ : S^{2} \to S^{2}$ be an anti-symplectic involution of $(S^{2}, ω)$ . We consider the product $(S^{2}, ω) \times (S^{2}, ω)$ endowed with the…

math.DG2020★ 3 cited

From flops to diffeomorphism groups

Gleb Smirnov

We exhibit many examples of closed complex surfaces whose diffeomorphism groups are not simply-connected and contain loops that are not homotopic to loops of symplectomorphisms.

math.SG2019

Symplectic triangle inequality

Vsevolod Shevchishin, Gleb Smirnov

We prove a non-squeezing result for Lagrangian embeddings of the real projective plane into blow-ups of the symplectic ball.

math.GT2018

Topology change and selection rules for high-dimensional $\Spin(1, n)_0$-Lorentzian cobordisms

Gleb Smirnov, Rafael Torres

We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the str…

math.SG2017

Elliptic diffeomorphisms of symplectic 4-manifolds

Vsevolod Shevchishin, Gleb Smirnov

We show that symplectically embedded $(- 1)$ -tori give rise to certain elements in the symplectic mapping class group of $4$ -manifolds. An example is given where such elements are p…

math.DS2015★ 2 cited

On the monodromy of almost toric fibrations on the complex projective plane

Gleb Smirnov

The monodromy of almost toric Lagrangian fibrations on the complex projective plane is described.

math.DS2013

Focus-focus singularities in classical mechanics

Gleb Smirnov

In this paper the local singularities of integrable Hamiltonian systems with two degrees of freedom are studied. The topological obstruction to the existence of focus-focus singula…

nlin.SI2013

The atlas of the diagrams for the generalization of the 4th Appelrot class of especially remarkable motions to a gyrostat in a double force field

Pavel E. Ryabov, Gleb E. Smirnov, Mikhail P. Kharlamov

For the system with two degrees of freedom, which is an analogue of the 4th Appelrot class for a gyrostat of the Kowalevski type in a double force field the problem of the classifi…

nlin.SI2012★ 3 cited

Types of critical points of the Kowalevski gyrostat in double field

M. P. Kharlamov, P. E. Ryabov, A. Y. Savushkin +1

The problem of motion of the Kowalevski type gyrostat in double force field is considered. According to the classification used in the theory of Liouville integrable Hamiltonian sy…

nlin.SI2010★ 1 cited

The existence conditions for periodic motions of the Kowalevski gyrostat in double force field

Irina I. Kharlamova, Gleb E. Smirnov

Consider the integrable problem of motion of a gyrostat with the Kowalevski type inertia tensor in a double force field. We study the special periodic motions (the rank 1 critical…

First integrals of dense hard-ball gases

Anti-self-dual blowups II

Anti-self-dual blowups

On Lagrangian tori in K3 surfaces

Symplectic mapping class groups of blowups of tori

Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants

Seidel's theorem via gauge theory

Infinitely many non-isotopic real symplectic forms on S2×S2

From flops to diffeomorphism groups

Symplectic triangle inequality

Topology change and selection rules for high-dimensional $\Spin(1, n)_0$-Lorentzian cobordisms

Elliptic diffeomorphisms of symplectic 4-manifolds

On the monodromy of almost toric fibrations on the complex projective plane

Focus-focus singularities in classical mechanics

The atlas of the diagrams for the generalization of the 4th Appelrot class of especially remarkable motions to a gyrostat in a double force field

Types of critical points of the Kowalevski gyrostat in double field

The existence conditions for periodic motions of the Kowalevski gyrostat in double force field

Infinitely many non-isotopic real symplectic forms on $S^{2} \times S^{2}$