Grant: L100192151
from 01/01/2022
to 31/12/2023
Grantor: Czech Academy of Sciences
Unilaterally constrained evolution
The project is supported by the "Programme to support prospective human resources – post Ph.D. candidates" funded by the Czech Academy of Sciences.
Objectives:
The main objective of the project is to establish a new theory of dynamics of sweeping processes with applications to natural sciences and network models. The directions (research activities) for the development of such a theory are:
1. A problem of elastoplastic evolution of mechanical networks: the case of large deformations for 2D and 3D networks and quasistatic solution as a limit of a dynamic problem.
2. Applications of non-convex sweeping process to piezoelectricity and magnetostriction.
3. Finite-time stability of the solutions of a sweeping process.
Grant: 22-01591S
from 01/01/2022
to 31/12/2024
Grantor: Czech Science Foundation
Mathematical theory and numerical analysis for equations of viscous newtonian compressible
Objectives:
Equations of compressible viscous fluids are important models in many applications. We will study the corresponding systems of partial differential equations from several points of view: existence theory and qualitative properties of solutions for different choices of boundary conditions (including open system), different types of domains (in particular varying in time), different types of solutions (weak, strong, dissipative) and different simplified models (in
particular, compressible primitive equations) as well as from the point of view of numerical mathematics (construction of benchmarks, numerical analysis of some methods, comparision of different numerical methods). The proposal of the project is based on a close collaboration of specialists from different mathematical disciplines.
Grant: L100192101
from 01/02/2021
to 31/01/2023
Grantor: Czech Academy of Sciences
Higher order scalar/vector-tensor theories of gravity and their spectrum of solutions
The project is supported by the "Programme to support prospective human resources – post Ph.D. candidates" funded by the Czech Academy of Sciences.
Project goal:
This research project is devoted to the study of new types of solutions in the context of DHOST theories. Work plan:
Year 1: Construction and study of new black holes solutions in the vector-tensor extension of DHOST theories by using the Kerr-Schild (KS) technique. We expect to find out a sector of quadratic theories admitting non-stealth solutions.
Year 2: Construction of planar black holes in DHOST theories by using axionic scalar fields, together with the study of holographic implications and the thermodynamics of these solutions. Exploring the exact gravitational wave solutions, specifically pp-waves, AdS waves including impulsive waves in DHOST theories. Studying general Kundt metrics and analysis of the corresponding algebraic classification.
Grant: GA21-02411S
from 01/01/2021
to 31/12/2023
Grantor: Czech Science Foundation
Solving ill posed problems in the dynamics of compressible fluids
Objectives:
The project focuses on mathematical models of compressible fluids that are ill-posed in the framework of the existing theory. A well known example is the Euler system describing a compressible perfect gas. By solving them we mean developing suitable consistent approximation, identifying the class of limits of approximate solutions, and designing appropriate numerical methods.
Matematický ústav AV ČR usiluje o HR Award - zavedení profesionálního řízení lidských zdrojů
Matematický ústav je přední českou věřejnou organizací, kterých posláním je vědecký výzkum v oblastech matematiky a jejích aplikací. Pro posílení jeho konkurenceschopnosti v mezinárodním kontextu je klíčové uvést dosavadní strategii řízení a rozvoje lidských zdrojů do souladu s Evropskou chartou pro výzkumné pracovníky, a tím umožnit získání ocenění HR Award. Pro ústav jde o mimořádnou příležitost, jak zkvalitnit a zprofesionalizovat péči o lidské zdroje, které jsou alfou a omegou jeho úspěchu.
Tento projekt je podpořen z operačního programu Výzkum, vývoj a vzdělávání, Výzva č. 02_18_054 pro Rozvoj kapacit pro výzkum a vývoj II v prioritní ose 2 OP, reg. č. CZ.02.2.69/0.0/0.0/18_054/0014664.
Grant: GX20-31529X
from 01/01/2020
to 31/12/2024
Grantor: Czech Science Foundation
Abstract convergence schemes and their complexities
Objectives:
Abstract convergence schemes are basic category-theoretic structures which serve as universes for studying infinite evolution-like processes and their limiting behavior. Convergence schemes endowed with extra structures provide an applicable framework for studying both discrete and continuous processes as well as their random variants.
The main goal of the project is unifying and extending several concepts from model theory, algebra, topology and analysis, related to generic structures. We propose studying selected topics within the framework of abstract convergence schemes, addressing questions on their complexity and classification. One of our inspirations is the theory of universal homogeneous models, where convergence of finite structures is involved. Another motivation is set-theoretic forcing, where a convergence scheme is simply a partially ordered set of approximations of some ``unreachable" objects, living outside of the universe of set theory.
Grant: GJ20-17488Y
from 01/01/2020
to 31/12/2022
Grantor: Czech Science Foundation
Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues
Objectives:
The 3 year project will bring together 4 promising mathematicians to build upon the successes of the classification programme for C*-algebras. There are 3 main goals:
A-Study structural properties and establish classification theorems for topological dynamical systems and their C*-algebras
B-Examine quantum group actions and the structure of their associated homogeneous spaces
C-Apply metric and geometric structures in C*-algebras to understand the fine structure of classifiable C*-algebras
Each goal consists of 3-4 concrete objectives. The expected output of 12-15 high quality research papers is outlined in an achievable schedule, divided into 4 month blocks. Already home to several researchers in C*-algebras, the Project's successful funding would position the Host Institute as a major European centre for C*-algebras. The team is highly active in the C*- algebra community and collaborates with world-leading experts, promising a successful outcome and efficient dissemination of results.
Symmetries, dualities and approximations in derived algebraic geometry and representation theory
Objectives:
The project focuses on new trends in homological algebra, represenation theory and algebraic geometry. In particular, we aim at studying and developing a theory of the exotic versions of derived categories and equivalences of these, studying derived commutative algebra, algebraic geometry and representation theory, and studying the homological algebra of and the structure theory for contramodules over topological rings, which were discovered only a few year ago. The applicants with collaborators recently published their results in distinguished mathematical journals (J. reine angew. Math., Invent. Math., Adv. Math., Mem. Amer. Math. Soc. and others), and the proposed project naturally builds on these results.
Grant: GA20-01074S
from 01/01/2020
to 31/12/2022
Grantor: Czech Science Foundation
Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers
Objectives:
The project deals with the numerical solution of several types of partial differential equations (PDEs) describing various practical phenomena and problems. The aim is to develop reliable and efficient numerical methods allowing to obtain approximate solutions of PDEs under the given tolerance using a minimal number of arithmetic operations. The whole process includes the proposals and analysis of discretization schemes together with suitable solvers for the solution of arising algebraic systems, a posteriori error estimation including algebraic errors and adaptive techniques balancing various error contributions. We focus on the use of adaptive higher-order schemes which allow to reduce significantly the number of necessary degrees of freedom required for the achievement of the prescribed accuracy. The adaptive mesh refinement must also take into account the properties of the resulting algebraic systems. The expected outputs of this projects are adaptive reliable and efficient numerical methods for the solution of the considered types of PDEs.
Grant: GA20-14736S
from 01/01/2020
to 31/12/2022
Grantor: Czech Science Foundation
Hysteresis modeling in mathematical engineering
Objectives:
Rate-independent hysteresis memory is known to occur in many physical processes such as magnetization of ferromagnetic materials, fluid flow through porous media, and phase transitions. Theoretical understanding of hysteresis mechanisms is of a key importance in engineering applications, where neglecting dissipative hysteresis effects in numerical predictions may lead to error accumulation and discrepancies with experiments. Most of the modern multifunctional materials used for high-precision devices exhibit hysteresis, which has to be taken into account in mathematical modeling. Surprisingly, hysteresis is also present in economic models. We focus here on mathematical and computational aspects of hysteresis in the whole range of applications. Special attention will be paid to the theoretical analysis of typical problems arising in dealing with smart materials, water-ice phase transitions in porous solids, and economics.