dr hab. Jarosław Buczyński
Wydział Matematyki, Informatyki i Mechaniki
Field of study:
mathematics
Zainteresowania badawcze:
My main research interests are in the area of Algebraic Geometry. It has relations and overlaps with many other areas of Mathematics and Science, including:
- Combinatorics,
- Representation Theory,
- Differential Geometry,
- Computational Complexity,
- Commutative Algebra,
- Algebraic Topology...
More specifically, the problems I am (or I have been) working on are related to the following notions and topics:
- secant varieties,
- Hilbert schemes, multigraded Hilbert schemes
- ranks of tensors and symmetric tensors (and partially symmetric ones, etc),
- toric varieties,
- Mori Dream spaces (MDS) and Cox rings,
- toric degenerations of Calabi-Yau varieties and K3 surfaces,
- contact Fano manifolds and LeBrun-Salamon conjecture,
- complex Legendrian varieties,
- Hilbert basis of a lattice cone,
- Tensor network states.
Tools I am using in my research include:
- homogeneous spaces and varieties with an open orbit (quasi-homogeneous varieties),
- toric geometry (and more generally, torus actions), and related combinatorics (lattices, cones, fans, polytopes, etc), and related algebra (Cox rings, so multigraded rings, etc),
- geometry and deformations of minimal rational curves on projective manifolds,
- computational algebraic geometry tools, such as Magma, ">http://magma.maths.usyd.edu.au/magma/handbook/">Magma,
- birational geometry,
- apolarity,
- cactus varieties and its analogues.
description of research interests:
My main research interests are in the area of Algebraic Geometry. It has relations and overlaps with many other areas of Mathematics and Science, including:
- Combinatorics,
- Representation Theory,
- Differential Geometry,
- Computational Complexity,
- Commutative Algebra,
- Algebraic Topology...
More specifically, the problems I am (or I have been) working on are related to the following notions and topics:
- secant varieties,
- Hilbert schemes, multigraded Hilbert schemes
- ranks of tensors and symmetric tensors (and partially symmetric ones, etc),
- toric varieties,
- Mori Dream spaces (MDS) and Cox rings,
- toric degenerations of Calabi-Yau varieties and K3 surfaces,
- contact Fano manifolds and LeBrun-Salamon conjecture,
- complex Legendrian varieties,
- Hilbert basis of a lattice cone,
- Tensor network states.
Tools I am using in my research include:
- homogeneous spaces and varieties with an open orbit (quasi-homogeneous varieties),
- toric geometry (and more generally, torus actions), and related combinatorics (lattices, cones, fans, polytopes, etc), and related algebra (Cox rings, so multigraded rings, etc),
- geometry and deformations of minimal rational curves on projective manifolds,
- computational algebraic geometry tools, such as Magma, ">http://magma.maths.usyd.edu.au/magma/handbook/">Magma,
- birational geometry,
- apolarity,
- cactus varieties and its analogues.
Realizowane projekty:
liczne projekty
research projects implemented:
many different projects
Słowa kluczowe:
secant varieties, contact manifolds, toric geometry
Key words:
secant varieties, contact manifolds, toric geometry
Contact:
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