About

I explore Deformation Theory using tools from stack theory to representation theory to combinatorics and computational tools such as Magma, M2. I work in particular on Hilbert schemes, Bialynicki-Birula decompositions, Macaulay duality and applications.
See my papers or my poster for details. If you want to discuss, just send me an email!

News

• The Hilbert scheme of infinite affine space and algebraic K-theory was accepted in JEMS.
• My friend and student Łukasz Sienkiewicz successfully defended his PhD on 1 Dec!
• The MSc thesis of my student Michał Szachniewicz (now in Oxford) is on arXiv. The thesis proves that the Hilbert schemes of points are nonreduced already for 13 points! All this subtly uses the BB decomposition.
• My joint paper with Klemen on Quot schemes and ADHM construction is out! We hope that it may shed light on some old problems in linear algebra and tensors, you might see my presentation for more info.

Teaching and outreach

• 2021-22 letni. Zaawansowane narzędzia geometrii algebraicznej (wykład mono).
• 2021-22 winter. Commutative Algebra.
• 2021-22 (całoroczne). Fundamenty geometrii algebraicznej (seminarium "Vakilowe")
• 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)