Publications and preprints
Perverse coherent sheaves on symplectic singularities. (2025) I. Dumanski, arXiv:2510.22541
K-theoretic Hikita conjecture for quiver gauge theories. (2025) I. Dumanski, V. Krylov, arXiv:2509.06226
A geometric approach to Feigin-Loktev fusion product and cluster relations in coherent Satake category (2024) I. Dumanski, International Mathematics Research Notices, 2024(22), pp.13988-14007.
On reduced arc spaces of toric varieties. (2025) I. Dumanski, E. Feigin, I. Makedonskyi, I. Makhlin, Algebra & Number Theory, 19(2), pp.313-363.
Beilinson–Drinfeld Schubert varieties and global Demazure modules. (2021) I. Dumanski, E. Feigin, M. Finkelberg. Forum of Mathematics, Sigma. doi:10.1017/fms.2021.36
Reduced arc schemes for Veronese embeddings and global Demazure modules. (2023) I. Dumanski, E. Feigin. Communications in Contemporary Mathematics, 25(08), p.2250034.
In preparation:
"Noncommutative resolutions of affine Schubert varieties and canonical basis for quantum affine group". I. Dumanski, V. Krylov
Recorded talks
Here are the recordings and slides for some of my talks
"Perverse coherent sheaves and cluster categorifications" at Perimeter Institute (video)
"Noncommutative resolutions and canonical bases" at Geometry and Physics seminar, Fields Institute, Toronto (video)
"From quantum loop group to coherent Satake category via fusion product" at M-seminar, online (video).
"Coherent Satake category and modules over quantum loop group" at the conference "Representation Theory and Related Geometry'', University of Georgia, Athens GA (slides).
"Cluster categorications and Feigin-Loktev fusion product" at the workshop "Quantum Structures in Lie Theory'', University of Virginia, Charlottesville VA (slides).
"Reduced structure of arc spaces" at the conference "Integer Partitions, Arc Spaces and Vertex Operators'' at Joint Mathematics Meeting 2024, San Francisco (slides).
"Schubert varieties in the Beilinson-Drinfeld Grassmannian" at Azat Miftakhov Days, online (video) (slides).
"Global Demazure modules" at the Aachen-Bochum-Cologne-Darstellungstheorie seminar, online (slides).
"Global Demazure modules" at the "Lie Algebras and Applications" seminar, HSE University, Moscow (video in Russian).