Research

My work is primarily focused on different aspects of geometry, and I work on the intersection of algebraic geometry, complex geometry and algebraic topology. The topics I research include:

equivariant cohomology theories;
topological invariants of algebraic varieties;
characteristic classes of singular spaces;
combinatorics of flag and Schubert varieties;
toric varieties and related commutative algebra.

Apart from the work I publish, I also enjoy thinking about homotopy theory, model structures, infinity-categories, intersection theory and moduli spaces.

Research papers

K. Rychlewicz, Variations on cohomology rings and zero schemes, October 2025.
K. Rychlewicz, Equivariant cohomology and rings of functions (PhD Thesis), June 2024. Also available on arXiv.
T. Hausel and K. Rychlewicz, Spectrum of equivariant cohomology as a fixed point scheme, in Épijournal Géom. Algébrique, 9 (2025), Article 1. Published version available here and on arXiv.
K. Rychlewicz, The positivity of local equivariant Hirzebruch class for toric varieties, in Bull. London Math. Soc., 53 (2021), 560–574. Preprint.
K. Rychlewicz, A bound on degrees of primitive elements of toric graph ideals, in Multigraded Algebra and Applications, Springer Proceedings in Mathematics & Statistics, 2018. Preprint.

Conferences, seminars and talks

Research Programme Elliptic Objects, von Neumann Algebras, and Functorial Field Theory, Bernoulli Center, EPFL, Switzerland, 6 – 17 July 2026, participant.
Schubert Seminar, online inter-university seminar, 10 November 2025, speaker.
Research Programme Representations, Moduli and Duality, Bernoulli Center, EPFL, Switzerland, 21 July – 22 August 2025, participant.
Conference Torus Actions and Characteristic Classes, Będlewo conference center, Poland, 1 – 7 June 2025, co-organizer.
Reading Seminar Cohomology of algebraic stacks, EPFL, summer semester 2025, co-organizer.
Bonn-Vienna block seminar: Equivariant cohomology, stable envelopes and big algebras, University of Bonn, 8 – 11 February 2025, speaker.
Workshop Modern Methods in Moduli, University of Luxembourg, 26 – 28 November 2024, speaker.
Summer School Interactions between Algebra, Equivariance, and Homotopy Theory, University of Regensburg, 24 – 28 June 2024, speaker.
Groups, Arithmetic & Algebraic Geometry Seminar, EPFL, Lausanne, Switzerland, 18 April 2024, speaker.
Workshop Singularity theory and hyperbolicity, University of Cambridge, UK, 18 – 22 March 2024, participant.
School Equivariant methods in geometry, University of Cambridge, UK, 8 – 12 January 2024, participant.
IMPANGA, Algebraic Geometry seminar of Institute of Mathematics of Polish Academy of Sciences, Warsaw, Poland, 15 December 2023, speaker.
Algebra and Geometry Seminar, Hong Kong University of Science and Technology, 6 November 2023, speaker.
Conference on Characteristic Classes and Singular Spaces, Kiel University, Germany, 18 – 22 September 2023, speaker.
Workshop Hodge and K-Theory meet Combinatorics, EPFL, Lausanne, Switzerland, 4 – 8 September 2023, speaker.
Workshop The Hitchin system, Langlands duality and mirror symmetry, ICMAT, Madrid, Spain 24 – 29 April 2023, participant.
Summer School Local Cohomology and related topics, KTH, Stockholm, Sweden, 1 – 5 August 2022, participant.
Summer School Representation theory and flag or quiver varieties, Université Paris Cité, Paris, France, 13 – 17 June 2022, participant.
Spring School Invariants in Algebraic Geometry, Institut de Mathématiques de Bourgogne, Dijon, France, 16 – 20 May 2022, participant.
40th Autumn School in Algebraic Geometry Binomial Ideals, Łukęcin, Poland, 3 – 9 September 2017, participant.
EMS Summer School on Multigraded Algebra and Applications, Moieciu de Sus, Romania, 17 – 24 August 2016, participant.