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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, co-advised with Pat Lank).
• Postdocs: Kriti Goel (2023-2025), Devlin Mallory (2024-2026, 2026-2028 as a Marie Skłodowska-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.

• Stability and deformation of F-singularities
  Alessandro De Stefani and Ilya Smirnov. Israel J. Math., 264(1), pp. 1-35, 2024.
• The theory of F-rational signature
  Ilya Smirnov and Kevin Tucker. J. Reine Angew. Math., 812, pp. 1-58, 2024.
• Effective generic freeness and applications to local cohomology
  Yairon Cid-Ruiz and Ilya Smirnov. J. Lond. Math. Soc. (2), 110(4), pp. Paper No. e12995, 31, 2024.
• Lower bounds on Hilbert-Kunz multiplicities and maximal F-signatures
  Jack Jeffries, Yusuke Nakajima, Ilya Smirnov, Kei-ichi Watanabe, and Ken-Ichi Yoshida. Math. Proc. Cambridge Philos. Soc., 174(2), pp. 247-271, 2023.
• Uniform Lech's inequality
  Linquan Ma and Ilya Smirnov. Proc. Amer. Math. Soc., 151(6), pp. 2387-2397, 2023.
• A transformation rule for natural multiplicities
  Jack Jeffries and Ilya Smirnov. Int. Math. Res. Not. IMRN, 2022(2), pp. 999-1015, 2022.
• Equimultiplicity Theory of Strongly F-regular rings
  Thomas Polstra and Ilya Smirnov. Michigan Math. J., 70(4), pp. 837-856, 2021.
• Decomposition of graded local cohomology tables
  Alessandro De Stefani and Ilya Smirnov. Math. Z, 297(1), pp. 1-24, 2021.
• Hilbert–Kunz multiplicities and F-thresholds
  Luis Núñez-Betancourt and Ilya Smirnov. Bol. Soc. Mat. Mex., 26(1), pp. 15-25, 2020.
• On the generalized Hilbert-Kunz function and multiplicity
  Hailong Dao and Ilya Smirnov. Israel J. Math., 237(1), pp. 155-184, 2020.
• Colength, multiplicity, and ideal closure operations
  Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Comm. Algebra, 48(4), pp. 1601-1607, 2020.
• On semicontinuity of multiplicities in families
  Ilya Smirnov. Doc. Math., 25, pp. 381-399, 2020.
• Continuity of Hilbert–Kunz multiplicity and F-signature
  Thomas Polstra and Ilya Smirnov. Nagoya Math. J., 239, pp. 322-345, 2020.
• Filter regular sequence under small perturbations
  Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Math. Ann., 378(1-2), pp. 243-254, 2020.
• Asymptotic Lech's inequality
  Craig Huneke, Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Adv. Math., 372, pp. 107296, 33, 2020.
• Equimultiplicity in Hilbert-Kunz theory
  Ilya Smirnov. Math. Z, 291(1-2), pp. 245-278, 2019.
• A generalization of an inequality of Lech relating multiplicity and colength
  Craig Huneke, Ilya Smirnov, and Javid Validashti. Comm. Algebra, 47, pp. 2436-2449, 2019.
• Hilbert-Kunz multiplicity of the powers of an ideal
  Ilya Smirnov. Proc. Amer. Math. Soc., 147(8), pp. 3331-3338, 2019.
• Lech's inequality, the Stückrad–Vogel conjecture, and uniform behavior of Koszul homology
  Patricia Klein, Linquan Ma, Pham Hung Quy, Ilya Smirnov, and Yongwei Yao. Adv. Math., 347, pp. 442-472, 2019.
• The multiplicity and the number of generators of an integrally closed ideal
  Hailong Dao and Ilya Smirnov. J. Singularities, 19, pp. 61-75, 2019.
• D-module and F-module length of local cohomology modules
  Mordechai Katzman, Linquan Ma, Ilya Smirnov, and Wenliang Zhang. Trans. Amer. Math. Soc., 370(12), pp. 8551-8580, 2018.
• Upper semi-continuity of the Hilbert-Kunz multiplicity
  Ilya Smirnov. Compos. Math., 152(3), pp. 477-488, 2016.
• Prime filtrations of the powers of an ideal
  Craig Huneke and Ilya Smirnov. Bull. Lond. Math. Soc., 47(4), pp. 585-592, 2015.
• Differential Krull dimension in differential polynomial extensions
  Ilya Smirnov. J. Algebra, 344, pp. 354-372, 2011.
• Colength, multiplicity, and ideal closure operations II
  Linquan Ma, Pham Hung Quy, and Ilya Smirnov. Michigan Math. J..
• An invitation to equimultiplicity of F-invariants
  Ilya Smirnov. .

Preprints

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