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Research area

• Commutative algebra, with a focus on interactions with algebraic geometry and singularity theory.

Employment

• Ramon y Cajal Fellow, BCAM – Basque Center for Applied Mathematics, 2022-now, tenure-track position funded by the Ministry of Science and Innovation.
• Ikerbasque Research Fellow, BCAM – Basque Center for Applied Mathematics, 2021-now, tenure-track position cofunded by the Ikerbasque Foundation.
• La Caixa Junior Leader Fellow, BCAM – Basque Center for Applied Mathematics, 2021-2022, funded by La Caixa Foundation.
• Researcher, KTH Royal Institute of Technology, 03-11.2021, funded by Swedish Research Council.
• Researcher, Charles University in Prague, 10.2020-03.2021.
• Postdoc, Stockholm University, 2018-2020, mentored by Boris Shapiro.
• Postdoc, University of Michigan, 2015-2018, mentored by Mel Hochster.

Education

• Undegraduate - Lomonosov Moscow State University, 2011. Evgeny Golod and Dmitry Trushin are responsible for my interest in commutative algebra.
• Graduate school - University of Kansas, moved to University of Virginia, PhD 2015, advised by Craig Huneke

Funding

• A grant in the Europa Excelencia Program of the Ministry of Science and Innovation, 2023-2025.
• Grants in the National Plan of the Ministry of Science and Innovation: 2022-2025, 2025-2029.
• Ikerbasque Research Fellowship, 2021-2026.
• Ramon y Cajal Fellowship, 2022-2027.
• La Caixa Junior Leader Fellowship Postdoctoral Fellowship, 2021-2024. Forfeited in 2022.
• Starting Grant, Swedish Research Council, 2021-2025. Forfeited in 2021.

Supervision

• PhD students: Joel Castillo-Rey (since 2023), Elias Guisado (since 2024).
• Postdocs: Kriti Goel (2023-2025), Devlin Mallory (2024-2026, 2026-2028 as a Marie-Curie fellow), Antonino Ficarra (2025-2027, Juan de la Cierva fellow).

Teaching

• Eight years of teaching experience at undergraduate level. Various calculus classes in Kansas, Virginia, and Michigan; Applied Linear algebra, Introduction to Probability in Michigan; Mathematical methods for economists in Stockholm. Practicals for Algebra I in Prague.
• Several graduate level lecture series at BCAM and research schools.

Publications

More information about these projects and ongoing projects is available in Research.

• Ilya Smirnov. Differential Krull dimension in differential polynomial extensions. Journal of Algebra, 344:354–372, 2011.
• Craig Huneke and Ilya Smirnov. Prime filtrations of the powers of an ideal. Bulletin of the London Mathematical Society, 47(4):585–592, 2015.
• Ilya Smirnov. Upper semi-continuity of the Hilbert-Kunz multiplicity. Compositio Mathematica, 152(3):477–488, 2016.
• Mordechai Katzman, Linquan Ma, Ilya Smirnov, and Wenliang Zhang. D-module and F-module length of some local cohomology modules. Transactions of the American Mathematical Society, 370(12):8551-8580, 2018.
• Craig Huneke, Ilya Smirnov, and Javid Validashti. A generalization of an inequality of Lech relating multiplicity and colength. Communications in Algebra, Special Issue in Honor of Gennady Lyubeznik, 47(6):2436-2449, 2019.
• Ilya Smirnov. Equimultiplicity in Hilbert-Kunz theory. Mathematische Zeitschrift, 291(1-2):245-278, 2019.
• Ilya Smirnov. Hilbert-Kunz multiplicity of the powers of an ideal. Proceedings of the American Mathematical Society, 147(8): 3331-3338, 2019.
• Patricia Klein, Linquan Ma, Pham Hung Quy, Ilya Smirnov, and Yongwei Yao. Lech's inequality, the Stückrad--Vogel conjecture, and uniform behavior of Koszul homology. Advances in Mathematics, 347:442-472, 2019.
• Hailong Dao and Ilya Smirnov. The multiplicity and the number of generators of an integrally closed ideal. Journal of Singularities, 19:61–75, 2019.
• Luis Núñez-Betancourt and Ilya Smirnov. Hilbert-Kunz multiplicity and F-thresholds. Boletín de la Sociedad Matemática Mexicana, 26(1): 15-25, 2020.
• Hailong Dao and Ilya Smirnov. On generalized Hilbert-Kunz function and multiplicity. Israel Journal of Mathematics., 237(1): 155–184, 2020.
• Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Colength, multiplicity, and ideal closure operations. Communications in Algebra, 48(4): 1601-1607, 2020.
• Ilya Smirnov. On semicontinuity of multiplicities in families. Documenta Mathematica, 25: 381-399, 2020.
• Thomas Polstra and Ilya Smirnov. Continuity of Hilbert-Kunz multiplicity and F-signature. Nagoya Mathematical Journal, 239:322-345, 2020. Erratum: Nagoya Mathematical Journal, 245: 229-231, 2022.
• Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Filter regular sequence under small perturbations. Mathematische Annalen, 378(1-2):243-254,2020.
• Alessandro De Stefani and Ilya Smirnov. Decomposition of graded local cohomology tables. Mathematische Zeitschrift, 297(1):1-24, 2021.
• Thomas Polstra and Ilya Smirnov. Equimultiplicity Theory of Strongly F-regular rings. Michigan Mathematical Journal, 70(4):837–856, 2021.
• Craig Huneke, Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Asymptotic Lech's inequality. Advances in Mathematics, 372:107296, 2020.
• Jack Jeffries and Ilya Smirnov. A transformation rule for natural multiplicities. International Mathematics Research Notices, 2022(2):999-1015, 2022.
• Jack Jeffries, Yusuke Nakajima, Ilya Smirnov, Kei-ichi Watanabe, Ken-ichi Yoshida. Lower bounds on Hilbert-Kunz multiplicities and maximal F-signatures. Mathematical Proceedings of the Cambridge Philosophical Society, 174(2):247-271, 2023.
• Linquan Ma and Ilya Smirnov. Uniform Lech's inequality. Proceedings of the American Mathematical Society, 151(6):2387-2397, 2023.
• Alessandro De Stefani and Ilya Smirnov. Stability and deformation of F-singularities. Israel J. Math., 264(1):1–35, 2024.
• Yairon Cid-Ruiz and Ilya Smirnov Effective generic freeness and applications to local cohomology. J. Lond. Math. Soc. (2), 110(4):Paper No. e12995, 31, 2024.
• Ilya Smirnov and Kevin Tucker. The theory of F-rational signature. Crelle's journal, 812:1–58, 2024.
• Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Colength, multiplicity, and ideal closure operations II. Michigan Math. Journal, accepted.
• Ilya Smirnov. An invitation to equimultiplicity of F-invariants. To appear in Contemporary Mathematics, a volume in honor of Hochster and Huneke.

Preprints

• Boris Shapiro, Ilya Smirnov, and Arkady Vaintrob. Around generalized zonotopal algebras of graphs.
• Alessandro De Stefani and Ilya Smirnov. Tight closure of products and F-rational singularities.
• Alessandro De Stefani, Luis Núñez-Betancourt, and Ilya Smirnov. The defect of the F-pure threshold.
• Aldo Conca, Alessandro De Stefani, Luis Núñez-Betancourt, and Ilya Smirnov. F-singularities of polynomials with square-free support.
• Igor Pak, Boris Shapiro, Ilya Smirnov, and Ken-ichi Yoshida. Hilbert–Kunz multiplicity of quadrics via Ehrhart theory.
• Linquan Ma and Ilya Smirnov. Lech–Mumford constant and stability of local rings.