About

My work is in the intersection of algebraic geometry and commutative algebra, frequently with a view towards applications. I am happy to use tools from infty-cats, stack theory to representation theory to combinatorics and computational tools such as M2. I work in particular on deformations of zero-dimensional objects, Bialynicki-Birula decompositions, Hilbert and Quot schemes, applications to tensors and secants varieties, applications to motivic homotopy theory etc.
See my papers or my poster for details. If you want to discuss, just send me an email!

News

• I put a list of open problems in zero-dimensional deformations on arXiv. Enjoy! Also thanks to Tony Iarrobino for the initial push.
• On 27 April 2023, I have been granted a habilitation.
• My joint paper with Joseph Landsberg and Arpan Pal on minimal border rank tensors is accepted in Mathematiche Annalen. The interesting part is that such tensors are algebraic: they come from a bilinear map between modules. Also they have a new invariant: 111-algebra, which is unexpected (there exist few such interesting invariants) was a small wonder to find.

Teaching and outreach

• 2023-24. Seminarium Fundamenty geometrii algebraicznej (seminarium "Vakilowe").
• 2023-24 winter. Complex manifolds.
• 2022-23 semestr letni. Teoria Liczb.
• 2022-23 winter. Commutative Algebra.
• Przeszłe edycje zajęć na UW
• Krótka notka "Jak uczyć się geometrii algebraicznej na UW"
• Strona kółka matematycznego, które prowadziłem w ILO Białystok (dużo zadań olimpijskich dla licealistów)
• Białynicki-Birula's article Some Properties of the Decompositions of Algebraic Varieties Determined by Actions of a Torus