Samarkand, Uzbekistan
September 11-20, 2023

International Summer School and Conference

13th Sompaty seminar
Thursday, February 17 at 9 am

Illia Karabash

TU Dortmund and IAMM of NAS of Ukraine

**Title of the talk:**A description of m-dissipative boundary conditions for Maxwell operators and its electrodynamics applications

Motivated by modeling of leaky optical cavities, we give a description of

all m-dissipative boundary conditions for Maxwell operators in Lipschitz domains.

If time allow us, it is planned to show applications of this description to Leontovich boundary conditions

and to the cases of degenerate and random impedance coefficients.

The talk is based on a joint research with Matthias Eller.

12th Sompaty seminar
Monday, January 24 at 11:30 am

Prof. Martina Hentschel

Institute for Physics, TU Chemnitz, Germany

**Title of the talk:**PT symmetry in mesoscopic systems

Short discussion
Monday, January 10 at 11:30 am

Short meeting

in order to coordinate our activities.

11th Sompaty seminar
Thursday, November 25 at 9am

Alexandra Antoniuk

Institute of Mathematics of the National Academy of Sciences of Ukraine

**Title of the talk:**🗎 Pseudo-differential equation with spatial p-adic variables and some of their applications

10th Sompaty seminar
Thursday, November 11 at 9am

Elvin I. Azizbayov

The Academy of Public Administration under the President of the Republic of Azerbaijan, Baku

**Title of the talk: **🗎 Nonlinear Inverse Problem for the Equation of Propagation of Longitudinal Waves with non-self-adjoint Boundary Conditions

9th Sompaty seminar
Thursday, October 21 at 9am

Carsten Trunk

Institut für Mathematik, Technische Universität Ilmenau

**Title of the talk: **

🗎 Sturm-Liouville, PT-symmetric operators and differential algebraic

8th Sompaty seminar
Thursday, September 30 at 9am

Jambul Yusupov

Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent

**Title of the talk: **Modeling and design of PT-symmetric networks: Quantum transport, soliton dynamics and dissipation effects

We discuss extension of PT-symmetric quantum physics and soliton theory to the case of networks. In particular, we provide an approach for designing

PT-symmetric quantum graphs. Also, we discuss the problem of sliton

dynamics in networks. Relation of the both problems to the issue of

dissipative networks will be also discussed.

7th Sompaty seminar
Thursday, September 9 at 9 am

Kateryna Pozharska

Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine

We will discuss the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. We study a certain weighted least squares algorithm that uses the so-called ”standard information”, i.e., finite number of function values at some points. The main advantage of our approach is that the nodes are taken at random w.r.t. a tailored distribution and simultaneously for the whole class of functions. We show that the considered deterministic algorithm leads to near optimal results in several relevant situations. We additionally apply a recently introduced sub-sampling technique to further reduce the sampling budget.

6th Sompaty seminar
Thursday, August 19 at 9am German time

Anar T. Assanova

Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

**Title of the talk:**

Constructive methods for solving nonlocal boundary value problems for integro-differential equations *PT*-symmetry

This talk is devoted to boundary value problems for Fredholm integro-differential equations and constructive methods for solving them. We will discuss the effectiveness of the Dzhumabaev parametrization method for solving nonlocal boundary value problems. We consider the questions on existence and uniqueness of solutions to boundary value problems for hyperbolic Fredholm integro-differential equations. We also present our recent research results on boundary value problems for Fredholm integro-differential equations and numerical and approximate methods for solving boundary value problems with parameter. We report about some results of boundary value problems for parabolic Fredholm integro-differential equations.

5th Sompaty seminar
Thursday, August 5 at 9am German time

Jürgen Prestin

Universität Lübeck

**Title of the talk:**

Multivariate Trigonometric Wavelets and Shearlets

4th Sompaty seminar
Thursday, July 22 at 9am German time

Fikret Aliev

Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

**Title of the talk:**🗎 Some mathematical problems and their solution for problem of oscillatory systems with liquid dampers

3rd Sompaty seminar
Thursday, July 1 at 9 am

Pavel Exner

Doppler Institute for Mathematical Physicsand Applied Mathematics, Prague
**Title of the talk:**
Quantum graphs: time-reversal non-invarianceand *PT*-symmetry
The talk concerns effects coming from a violation of time-reversal symmetryin the vertex coupling of quantum graphs, focusing on the situation when theasymmetry is maximal at a fixed energy. It is shown that such a coupling hasa topological property: scattering at the vertex in the high-energy regimedepends substantially on the vertex parity. We explore implications of thisfact for spectral and transport properties in several classes of graphs, bothfinite and infinite periodic ones. We also identify a class of vertex couplingexhibiting a nontrivialPT-symmetry despite being self-adjoint. The resultscome from a common work with Marzieh Baradaran, Jiří Lipovský, andMiloš Tater.

2nd Sompaty seminar
Thursday, June 10 at 9am German time

Oleksandr Burylko

Leading researcher, Dep. of Differential equations and oscillation theory of the Institute of Mathematics NAS of Ukraine

**Title of the talk:****🗎** Collective dynamics in networks of phase oscillators

The talk is dedicated to the description of collective dynamics in the networks of phase oscillators of the Kuramoto type. I plan to show how the architecture and symmetry of the network, individual dynamics, and the interaction functions affect the emergence, structure, stability, and bifurcations of different collective regimes (synchronization, clustering, splay states, antiphase regimes, slow switching, chimera state, etc.).

1st Sompaty seminar
Thursday, May 20 at 9am German time

Davron Matrusulov

Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent

**Title of the talk:****🗎** Tunable quantum networks: Modeling and design transparent and PT-symmetric quantum graphs

In this talk I will briefly introduce the concept of quantum graph as model of branched quantum structures and discuss how to make their branching points (vertices) transparent, i.e. providing reflectionless transmission of waves/particles through these points. Also, I willl introduce concept of PT-symmetric (non-Hermitian) quantum graphs and provide sketch for their experiemntal realization.

13th Sompaty seminar
Thursday, February 17 at 9 am

Illia Karabash

TU Dortmund and IAMM of NAS of Ukraine
**Title of the talk:
**A description of m-dissipative boundary conditions for Maxwell operators and its electrodynamics applications

Meeting ID: 917 4920 9940
Passcode: 061376

Motivated by modeling of leaky optical cavities, we give a description of

all m-dissipative boundary conditions for Maxwell operators in Lipschitz domains.

If time allow us, it is planned to show applications of this description to Leontovich boundary conditions

and to the cases of degenerate and random impedance coefficients.

The talk is based on a joint research with Matthias Eller.

12th Sompaty seminar
Monday, January 24 at 11:30 am

Prof. Martina Hentschel

Institute for Physics, TU Chemnitz, Germany

**Title of the talk:**PT symmetry in mesoscopic systems

Short discussion
Monday, January 10 at 11:30 am

Short meeting

11th Sompaty seminar
Thursday, November 25 at 9am

Alexandra Antoniuk

Institute of Mathematics of the National Academy of Sciences of Ukraine

**Title of the talk:**🗎 Pseudo-differential equation with spatial p-adic variables and some of their applications

10th Sompaty seminar
Thursday, November 11 at 9am

Elvin I. Azizbayov

The Academy of Public Administration under the President of the Republic of Azerbaijan, Baku

**Title of the talk: **🗎 Nonlinear Inverse Problem for the Equation of Propagation of Longitudinal Waves with non-self-adjoint Boundary Conditions

9th Sompaty seminar
Thursday, October 21 at 9am

Carsten Trunk

Institut für Mathematik, Technische Universität Ilmenau

**Title of the talk: **

🗎 Sturm-Liouville, PT-symmetric operators and differential algebraic

8th Sompaty seminar
Thursday, September 30 at 9am

Jambul Yusupov

Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent

**Title of the talk: **Modeling and design of PT-symmetric networks: Quantum transport, soliton dynamics and dissipation effects

We discuss extension of PT-symmetric quantum physics and soliton theory to the case of networks. In particular, we provide an approach for designing

PT-symmetric quantum graphs. Also, we discuss the problem of sliton

dynamics in networks. Relation of the both problems to the issue of

dissipative networks will be also discussed.

7th Sompaty seminar
Thursday, September 9 at 9 am

Kateryna Pozharska

Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine

We will discuss the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. We study a certain weighted least squares algorithm that uses the so-called ”standard information”, i.e., finite number of function values at some points. The main advantage of our approach is that the nodes are taken at random w.r.t. a tailored distribution and simultaneously for the whole class of functions. We show that the considered deterministic algorithm leads to near optimal results in several relevant situations. We additionally apply a recently introduced sub-sampling technique to further reduce the sampling budget.

6th Sompaty seminar
Thursday, August 19 at 9am German time

Anar T. Assanova

Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

**Title of the talk:**

Constructive methods for solving nonlocal boundary value problems for integro-differential equations *PT*-symmetry

This talk is devoted to boundary value problems for Fredholm integro-differential equations and constructive methods for solving them. We will discuss the effectiveness of the Dzhumabaev parametrization method for solving nonlocal boundary value problems. We consider the questions on existence and uniqueness of solutions to boundary value problems for hyperbolic Fredholm integro-differential equations. We also present our recent research results on boundary value problems for Fredholm integro-differential equations and numerical and approximate methods for solving boundary value problems with parameter. We report about some results of boundary value problems for parabolic Fredholm integro-differential equations.

5th Sompaty seminar
Thursday, August 5 at 9am German time

Jürgen Prestin

Universität Lübeck

**Title of the talk:**

Multivariate Trigonometric Wavelets and Shearlets

4th Sompaty seminar
Thursday, July 22 at 9am German time

Fikret Aliev

Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

**Title of the talk:**🗎 Some mathematical problems and their solution for problem of oscillatory systems with liquid dampers

3rd Sompaty seminar
Thursday, July 1 at 9 am

Pavel Exner
The talk concerns effects coming from a violation of time-reversal symmetryin the vertex coupling of quantum graphs, focusing on the situation when theasymmetry is maximal at a fixed energy. It is shown that such a coupling hasa topological property: scattering at the vertex in the high-energy regimedepends substantially on the vertex parity. We explore implications of thisfact for spectral and transport properties in several classes of graphs, bothfinite and infinite periodic ones. We also identify a class of vertex couplingexhibiting a nontrivialPT-symmetry despite being self-adjoint. The resultscome from a common work with Marzieh Baradaran, Jiří Lipovský, andMiloš Tater.

Doppler Institute for Mathematical Physicsand Applied Mathematics, Prague

**Title of the talk:**

Quantum graphs: time-reversal non-invarianceand *PT*-symmetry

2nd Sompaty seminar
Thursday, June 10 at 9am German time

Oleksandr Burylko

Leading researcher, Dep. of Differential equations and oscillation theory of the Institute of Mathematics NAS of Ukraine

**Title of the talk:****🗎** Collective dynamics in networks of phase oscillators

The talk is dedicated to the description of collective dynamics in the networks of phase oscillators of the Kuramoto type. I plan to show how the architecture and symmetry of the network, individual dynamics, and the interaction functions affect the emergence, structure, stability, and bifurcations of different collective regimes (synchronization, clustering, splay states, antiphase regimes, slow switching, chimera state, etc.).

1st Sompaty seminar
Thursday, May 20 at 9am German time

Davron Matrusulov

Laboratory for Advanced Studies, Turin Polytechnic University in Tashkent

**Title of the talk:****🗎** Tunable quantum networks: Modeling and design transparent and PT-symmetric quantum graphs

In this talk I will briefly introduce the concept of quantum graph as model of branched quantum structures and discuss how to make their branching points (vertices) transparent, i.e. providing reflectionless transmission of waves/particles through these points. Also, I willl introduce concept of PT-symmetric (non-Hermitian) quantum graphs and provide sketch for their experiemntal realization.

The planned 3 thematic workshops and the 2 summer schools

The planned 3 thematic workshops and the 2 summer schools

2023

**Mathematics for the Micro/Nano-World**

(mit-term meeting)

Public Lecture

Proceedings

2024

2025

**Spectral Problems, Optimization and Applications**

(final meeting)

Public Lecture

Proceedings

Main networking activities

Main networking activities

We will publish the proceedings of the above-mentioned workshops as special issues with golden open access in a journal of high reputation.

This relates to knowledge sharing through collaborative web-based project work. The online database of the SOMPATY project will include a set of research databases, which will be continuously updated by the consortium participants for shared use.

- Preprints and Drafts
- workshop proceedings, public lectures, workshop lectures, models, programme code, information about the summer schools and outreach activities.
- Platform for collaborative research

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