Семинары проходят по средам, в 19:20 либо очно в аудитории 303, либо в зуум.

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ОСЕНЬ 2026

14 октября 2026 (среда), 19:20, семинар пройдёт полностью в Zoom'е:
Meeting ID: 88 17 12 1842
Passcode можно узнать по почте seminar@gdeq.org
Докладчик: К.П. Дружков
Тема: Computational algorithms for invariant reduction of variational forms

Язык доклада: английский

Аннотация:
Аннотация: Symmetry reductions of partial differential equations inherit more geometric structures than other types of reductions: invariant conservation laws, presymplectic structures, internal Lagrangians, and, under suitable conditions, Hamiltonian structures of the original system descend to its symmetry reduction through the mechanism of invariant reduction. Reductions of all these structures can often be described in terms of variational forms. We will discuss computational algorithms that carry out reductions of variational forms explicitly.

7 октября 2026 (среда), 19:20, семинар пройдёт очно в Независимом университете, комн. 303, одновременно будет трансляция в в Zoom'е:
Meeting ID: 88 17 12 1842
Passcode можно узнать по почте seminar@gdeq.org
Докладчик: В.В. Лычагин
Тема: Thermodynamics, jets geometry and phase transitions

Язык доклада: английский

Аннотация:
In this talk, we will discuss equations of state and phase transitions in thermodynamics, as well as their relationship to the geometry of jet spaces and differential equations.

The equations of state give a description of the thermodynamic media under consideration and, in the simplest case, are geometrically realized as Legendre manifolds in the contact space. This corresponds to first-order thermodynamics, and phase transitions of the 1st order correspond to the singularities of their projection onto the space of intensive quantities, and thus their study is based on Arnold's theory of the singularities of projections of Legendre and Lagrangian manifolds.

In practice, it is sometimes more convenient to set equations of state by thermodynamic quantities of the second and higher orders, which means a transition from contact geometry to the geometry of the spaces of jets of the second and higher order. This will be discussed in the talk, and the relationship of the equations of state with overdetermined systems of partial differential equations and with integral manifolds of the Cartan distribution is shown.

If time allows, the relationship between second- and higher-order phase transitions and the singularities given by integral manifolds of the Cartan distribution will be considered.

The proposed approach will also be illustrated by examples from thermodynamics.

30 сентября 2026 (среда), 19:20, семинар пройдёт очно в Независимом университете, комн. 303, одновременно будет трансляция в в Zoom'е:
Meeting ID: 88 17 12 1842
Passcode можно узнать по почте seminar@gdeq.org
Докладчик: М.В. Павлов
Тема: Local Lagrangian densities and 3D integrable systems

Язык доклада: английский

Аннотация:
We discuss the existence of local Lagrangian densities for integrable systems in three dimensions.

Our Observation: A few members of the Darboux-KP hierarchy possess local Lagrangian densities only.

These examples will be presented and discussed.

23 сентября 2026 (среда), 19:20, семинар пройдёт очно в Независимом университете, комн. 303, одновременно будет трансляция в в Zoom'е:
Meeting ID: 88 17 12 1842
Passcode можно узнать по почте seminar@gdeq.org
Докладчик: О.И. Морозов
Тема: A Lax representation, symmetries, and conservation laws for the three-dimensional Euler-Helmholtz equations

Язык доклада: английский

Аннотация:
I will consider the three-dimensional Euler-Helmholtz equations for an inviscid incompressible fluid and reformulate them in a vorticity-type form by introducing a vector potential. I will exhibit a Lax representation with a non-removable parameter for the resulting system. I will discuss local symmetries and conservation laws of the system. Using the Lax representation, I will derive a shadow of a cosymmetry and find nonlocal conservation laws via the construction of the canonical conservation law on the Whitney sum of the tangent and cotangent coverings. Finally, I will present a Bäcklund transformation between the tangent and cotangent coverings and describe its action on local symmetries and local cosymmetries.

16 сентября 2026 (среда), 19:20, семинар пройдёт очно в Независимом университете, комн. 303, одновременно будет трансляция в в Zoom'е:
Meeting ID: 88 17 12 1842
Passcode можно узнать по почте seminar@gdeq.org
Докладчик: А.В. Михайлов
Тема: Finite dimensional reductions of integrable differential-difference equations

Язык доклада: английский

Аннотация:
Integrable partial differential equations, such as the Korteweg-de Vries (KdV) equation, admit infinite hierarchies of commuting higher symmetries. Their symmetry reductions give rise to integrable finite-dimensional dynamical systems that are solvable in terms of Abelian functions. This observation underlies the finite-gap integration method for the KdV equation, introduced by S.P. Novikov and subsequently extended to a wide class of integrable systems. In this paper, we introduce a new and more general class of reductions for integrable differential-difference equations, leading to integrable finite-dimensional systems in both commutative and noncommutative settings. The reduction constraints define integrable maps that enable solutions of the reduced systems to be extended to solutions of the corresponding differential-difference equations. The construction is illustrated using the Volterra and Toda hierarchies.