Research of Jarosław Buczyński
My main research interests are in the area of Algebraic Geometry.
It has relations and overlaps with many other areas of Mathematics and
More specifically, the problems I am (or I have been) working on are
related to the following notions and topics:
- Representation Theory,
- Differential Geometry,
- Computational Complexity,
- Commutative Algebra,
- Algebraic Topology...
Tools I am using in my research include:
- 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.
- homogeneous spaces and varieties with an open orbit
- toric geometry (and more generally, torus actions), and related combinatorics (lattices, cones, fans,
polytopes, etc), and related algebra (Cox rings, so multigraded rings,
- geometry and deformations of minimal rational curves on projective manifolds,
- computational algebraic geometry tools, such as Magma,
- birational geometry,
- cactus varieties and its analogues.