Grants
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Grant: GA23-05148S
from 01/01/2023 to 31/12/2025
Grantor: Czech Science Foundation - Homological and structural theory in geometric contexts
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Objectives:
The project is focused on the study of objects originating in algebraic geometry and representation theory and their homological and structural properties. We are concerned with properties of both classical and recently discovered non-conventional derived categories and conditions for their equivalence as well as with homological dualities in semiinfinite algebraic geometry (in the form of formal and ind-schemes), homological and geometric approach to noncommutative algebras (coming for instance from variants of Fukaya categories) and a structural theory of the corresponding representations or (co)sheaves of representations. The project also aims at enhancing the long-term and fruitful collaboration with several European algebra centers and contributing to graduate education at MFF UK in new areas of contemporary mathematics. -
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Grant: GA23-06159S
from 01/01/2023 to 31/12/2025
Grantor: Czech Science Foundation - Vortical structures: advanced identification and efficient numerical simulation
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Objectives:
Advanced analysis and description of vortical structures aiming at:
- development of vortex-identification methods,
- spatio-temporal analysis,
- efficient numerical methods based on parallel immersed boundary adaptive FEM,
- high-resolution flow simulations,
- experimental measurements. -
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Grant: GA23-04683S
from 01/01/2023 to 31/12/2025
Grantor: Czech Science Foundation - Compactness in set theory, with applications to algebra and graph theory
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Objectives:
The goal of the project is to produce significant advances in the study of compactness in set theory and the application of set theoretic methods to questions from graph theory and homological algebra, and to foster collaboration, both locally and internationally, to achieve these aims. -
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Grant: GA23-04825S
from 01/01/2023 to 31/12/2025
Grantor: Czech Science Foundation - Logic and unsatisfiability
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Objectives:
We aim to show that increasing logical depth can decrease proof size; to improve logical characterizations of combinatorial proof systems and search problems, and vice versa; to show lower bounds on algebraic proof systems and systems from SAT solving; to develop mathematics over very weak axioms. -
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Grant: GA23-04720S
from 01/01/2023 to 31/12/2025
Grantor: Grant Agency of the Czech Republic - Fine properties of functions, operators and function spaces
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The main goal of the project will be solving open problems concerning fine properties of functions belonging to specific function spaces and their applications in the theory of approximations. We will put emphasis on finding optimal (not improvable) structures within certain categories.
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