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+34 946 567 842
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+34 946 567 842
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ismirnov@bcamath.org
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Ikerbasque profileI am a Ramón y Cajal and Ikerbasque Research Fellow at BCAM since 2022. Personal webpage.
My principal research area is local algebra; loosely speaking this means that I study singularities, as local rings, using techniques of commutative algebra. A particular way to do so is via numerical invariants, numbers that are supposed to represent an aspect of the complexity.

The theory of Frational signature
(2024)

Lower bounds on HilbertKunz multiplicities and maximal Fsignature
(2022)ABSTRACT. Hilbert–Kunz multiplicity and Fsignature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...

Uniform Lech's inequality
(2022)Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(Rred) > 1, then the classical Lech’s inequality can be improved uniformly for all mprimary ideals, that is, there exists ε > 0 such that e(I) ...

Uniform Lech's inequality
(2022)Let (R,m) be a Noetherian local ring, and let M be a finitely generated Rmodule of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...
School on Commutative Algebra and Algebraic Geometry in Prime Characteristics, ICTP Trieste, May 25, 2023.
BCAM Severo Ochoa course "Introduction to multiplicity theory" Spring 2023.
RGAS School on Singularities, IMUS Sevilla, January 812, 2024.