Dr. Natalia Tsilevich

• Asymptotics of higher Lie characters (with R.M.Adin and Y.Roichman).
arXiv:2509.12904 (2025).
• GL(n)-dependence of matrices (with Y.Manor).
arXiv:2510.13676 (2025).
• The Schur-Weyl graph and Thoma's theorem (with A.M.Vershik).
Funct. Anal. Appl. 55, No. 3, 198-209 (2021).
• Ergodicity and totality of partitions associated with the RSK correspondence (with A.M.Vershik).
Funct. Anal. Appl. 55, No. 1, 26-33 (2021).
• The intrinsic hyperplane arrangement in an arbitrary irreducible representation of the symmetric group (with A.M.Vershik and S.Yuzvinsky).
Arnold Mathematical Journal 6 (2020), 173-187.
• Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form (with A.M.Vershik).
J. Math. Sci. (N.Y.) 247 (2020), 657-662.
• On the decomposition of tensor representations of symmetric groups (with P.P.Nikitin and A.M.Vershik).
Algebras and Representation Theory 22, No. 4, 895-908 (2019).
• On the dual complexity and spectra of some combinatorial functions.
J. Math. Sci. (N.Y.) 232, No. 2 (2018), 170-176.
• On the relation of some combinatorial functions to representation theory (with A.M.Vershik).
Funct. Anal. Appl. 51, No. 1, 22-31 (2017).
• The serpentine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $\widehat{sl}_2$ (with A.M.Vershik).
Lett. Math. Phys. 105, No. 1, 11-25 (2015).
• Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator (with A.M.Vershik).
Comm. Math. Phys. 327, No. 3, 873-885 (2014).
• On the behavior of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits.
J. Math. Sci. (N.Y.) 181 (2012), 914-920.
• Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case.
J. Math. Sci. (N.Y.) 174 (2011), 58-70.
• Induced representations of the infinite symmetric group (with A.M.Vershik).
Pure Appl. Math. Quart. 3, No. 4 (2007), 1005-1026.
• Induced representations of the infinite symmetric group and their spectral theory (with A.M.Vershik).
Doklady Mathematics 75, No. 1 (2007), 1-4.
• Markov measures on Young tableaux and induced representations of the infinite symmetric group (with A.M.Vershik).
Prob. Theory Appl. 51, No. 1 (2006), 211-223.
• On different models of representations of the infinite symmetric group (with A.M.Vershik).
Adv. Appl. Math. 37, 526-540 (2006).
• Quantum inverse scattering method for the q-boson model and symmetric functions.
Funct. Anal. Appl. 40, No. 3 (2006), 207-217.
• On the Fourier transform on the infinite symmetric group (with A.M.Vershik).
J. Math. Sci. (N.Y.) 138, No. 3 (2006), 5663-5673.
• Fock factorizations, and decompositions of the L2 spaces over general Levy processes (with A.M.Vershik).
Russian Math. Surveys 58, No. 3 (2003), 427-472.
• Remarks on the Markov-Krein identity and quasi-invariance of the gamma process (with A.M.Vershik and M.Yor).
J. Math. Sci. (N.Y.) 121, No. 3 (2004), 2303-2310.
• On the simplest split-merge operator on the infinite-dimensional simplex.
PDMI preprint 03/2001, Steklov Institute of Mathematics at St.Petersburg, 2001.
• An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process (with A.M.Vershik and M.Yor).
J. Funct. Anal. 185, No. 1 (2001), 274-296.
• Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures (with A.M.Vershik).
C. R. Acad. Sci. Paris 329, Serie I (1999), 163-168.
• Stationary random partitions of positive integers.
Prob. Theory Appl. 44, No. 1 (2000), 60-74.
• The Markov-Krein correspondence in several dimensions (with S.V.Kerov).
J. Math. Sci. (N.Y.) 121, No. 3 (2004), 2345-2359.
• Distribution of the mean value for certain random measures.
J. Math. Sci. (N.Y.) 96, No. 5 (1999), 3616-3623.
• Stick breaking process generates virtual permutations with Ewens distribution (with S.V.Kerov).
J. Math. Sci. (N.Y.) 87, No. 6 (1997), 4082-4093.
• Distribution of cycle lengths of infinite permutations.
J. Math. Sci. (N.Y.) 87, No. 6 (1997), 4072-4081.

Academic Appointments:
2025-present: Braude College of Engineering, Senior Lecturer.2024-2025: Bar-Ilan University, Shapira Research Associate.2022-2024: University of Haifa, Shapira Research Associate.2001-2022: St.Petersburg Department of  Steklov Institute of Mathematics, Senior Researcher (tenured).1999-2020: St.Petersburg State University, Associate Professor.

Short-Term Research Visits:
2022: Weizmann Institute of Sciences, Rehovot, Israel.
2010: Northeastern University, Boston, USA.
2003: Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
2001: University of Bielefeld, Bielefeld, Germany.
2000: University of Bielefeld, Bielefeld, Germany.
1998: Weizmann Institute of Sciences, Rehovot, Israel.
1997: Institut de Mathématiques de Luminy, Marseille, France.

Teaching Experience:
Braude College of Engineering: Complex Functions, Linear Algebra.
University of Haifa: Selected Topics in Geometry, Enumerative Combinatorics.
Petersburg University, Department of Mathematics and Computer Science: Symmetric Functions, Representation Theory of Symmetric Groups
Petersburg University, Department of Mathematics and Mechanics: Complex Analysis, Ergodic Theory, Involution Algebras, Real Analysis.

Awards:
1999: Young Mathematician Prize of the St.Petersburg Mathematical Society.

Professional Membership:
1998-present: St.Petersburg Mathematical Society.

Editorial Boards:
2014-present: European Journal of Mathematics, editor.
2007-2022: Notes of Mathematical Seminars of St.Petersburg Department of Steklov Institute of Mathematics, coeditor for the series Representation Theory,
Dynamical Systems, Combinatorial Methods.
2010-2014: Central European Journal of Mathematics, editor.

My favorite professional hobby is translating math and popular science books.
Russian to English translations:
• B.Makarov and A.Podkorytov, Smooth Functions and Maps. Springer, 2020.
• S.Lvovski, Principles of Complex Analysis. Springer, 2020.
• S.Natanzon, Complex Analysis, Riemann Surfaces and Integrable Systems. Springer, 2019.
• M.E.Kazaryan, S.K.Lando, and V.V.Prasolov, Algebraic Curves: Towards Moduli Spaces. Springer, 2018.
• B.Makarov and A.Podkorytov, Real Analysis: Measures, Integrals, and Applications (Chapters 1-4, Appendices). Springer, 2013.
• S.V.Kerov, Asymptotic Representation Theory of the Symmetric Group and its Applications in Analysis. Translations of Mathematical Monographs, Vol. 219. American Mathematical Society, 2003.

English to Russian translations:
• H.Weyl, Mind and Nature. MCCME, Moscow, 2019.
• P.Etingof et al., Introduction to Representation Theory. MCCME, Moscow, 2019.
• S.L.Glashow, From Alchemy to Quarks: The Study of Physics as a Liberal Art. MCCME, Moscow, 2018.
• M.Gromov, The Ring of Mysteries: Universe, Mathematics, Mind. MCCME, Moscow, 2017.
• T.Tao, Structure and Randomness. MCCME, Moscow, 2014.
• M.L.Mehta, Random Matrices. MCCME, Moscow, 2012.
• D.Fuchs and S.Tabachnikov, Mathematical Omnibus (Chapters 3 and 8). MCCME, Moscow, 2011.
• D.Mumford, C.Series, and D.Wright, Indra's Pearls: The Vision of Felix Klein (Introduction, Chapters 1 and 2). MCCME, Moscow, 2011.
• J.F.C.Kingman, Poisson Processes. MCCME, Moscow, 2007.
• R.Stanley, Enumerative Combinatorics, Vol. 2 (partially). Mir, Moscow, 2005.