Almaty, Kazakhstan September 11-18, 2024
International Summer School (Sept 11-14) and Conference (Sept 16-18)
on
Evolution Equations, Approximation and Spectral Optimization
13th Sompaty seminar Thursday, February 17 at 9 am
12th Sompaty seminar Monday, January 24 at 11:30 am
Short discussion Monday, January 10 at 11:30 am
11th Sompaty seminar Thursday, November 25 at 9am
10th Sompaty seminar Thursday, November 11 at 9am
9th Sompaty seminar Thursday, October 21 at 9am
8th Sompaty seminar Thursday, September 30 at 9am
7th Sompaty seminar Thursday, September 9 at 9 am
6th Sompaty seminar Thursday, August 19 at 9am German time
5th Sompaty seminar Thursday, August 5 at 9am German time
4th Sompaty seminar Thursday, July 22 at 9am German time
3rd Sompaty seminar Thursday, July 1 at 9 am
2nd Sompaty seminar Thursday, June 10 at 9am German time
1st Sompaty seminar Thursday, May 20 at 9am German time
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
 in order to coordinate our activities.
 
Meeting ID: 917 4920 9940
Passcode: 061376
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

Title of the talk: 
Sampling recovery of multivariate functions

 

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

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 

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

The planned 3 thematic workshops and the 2 summer schools
The planned 3 thematic workshops and the 2 summer schools
2023
#Tash

Tashkent

Mathematics for the Micro/Nano-World
(mit-term meeting)
Public Lecture
Proceedings

Summer School
2024
#Alm

Almaty

Computational Methods and Approcximation
Public Lecture
Proceedings

Summer School
2025
#Baku

Baku

Spectral Problems, Optimization and Applications
(final meeting)
Public Lecture
Proceedings

Main networking activities
Main networking activities
Proceedings

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

Web-based knowledge exchange via an on-line database

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