Contact:
École Polytechnique,
CMLS, Office: 06.1006
Email: finski.siarhei(at)gmail.com
siarhei.finski(at)polytechnique.edu
Position:
I am a researcher (chargé de recherche, CNRS) in Center of Mathematics Laurent Schwartz, École Polytechnique. From September 2019 to October 2021, I was as a postdoctoral researcher in Université Grenoble Alpes, France, working under the direction of Jean-Pierre Demailly. Prior to that I was a graduate student in Université Paris Diderot, France, working under the direction of Xiaonan Ma.
Research interests:
I am mainly interested in global analysis on manifolds and complex geometry. Based on the methods from those areas, my work relates to Atiyah-Singer theorem, local index theory, semi-classical analysis and probability theory.
Currently I'm working on extension problems in complex geometry and their applications.
Publications and preprints:
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The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds, 42 p.
ArXiv: 2207.02761, 2022. -
Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions, 52 p.
ArXiv: 2201.04102, 2022. -
Semiclassical Ohsawa-Takegoshi extension theorem and asymptotics of the orthogonal Bergman kernel, 72 p.
ArXiv: 2109.06851, 2021. -
On Monge-Ampère volumes of direct images,
Int. Math. Res. Not., Vol. 2022, No. 16, pp. 12072-12095, 2022. ArXiv: 2010.01839. -
On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities,
J. London Math. Soc., 106:1539–1579, 2022. ArXiv: 2009.13107. -
Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion,
Math. Z., 301 (4): 3285-3343, 2022. ArXiv: 2001.05162. -
Finite difference method on flat surfaces with a flat unitary vector bundle,
J. Geom. Anal., 32, No. 11, Paper No. 274, 37 p., 2022. ArXiv: 2001.04862. -
Determinants of Laplacians on discretizations of flat surfaces and analytic torsion,
C. R. Acad. Sci. Paris, 358 (6): 743-751, 2020. -
Quillen metric for singular families of Riemann surfaces with cusps and compact perturbation theorem, 40 p.
ArXiv: 1911.09087, 2019, to appear in Math. Res. Lett. -
Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem,
Adv. Math., 375, 2020, 47 p., 107409. ArXiv: 1812.11739. -
Analytic torsion for surfaces with cusps I. Compact perturbation theorem and anomaly formula,
Commun. Math. Phys., 378 (12): 1713 – 1774, 2020. ArXiv: 1812.10442. -
On the full asymptotics of analytic torsion,
J. Funct. Anal., 275 (12): 3457 - 3503, 2018. ArXiv: 1705.02779.
Proceedings:
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Quillen metric theory for surfaces with cusps, 13 p.
2020, Accepted in Actes du séminaire Théorie Spectrale et Géométrie.
Conference talks:
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2022"On the metric structure of section rings".
Noncommutative geometry and Geometric analysis, Villa de Leyva, Colombia. -
2022"On the metric structure of section rings".
Complex Geometry, Dynamical Systems and Foliation Theory, Luminy, France. Slides, Video. -
2022"Semiclassical Ohsawa-Takegoshi extension theorem and applications".
Complex Geometry and Dynamical Systems, Oberwolfach, Germany. Slides. -
2022"Semiclassical Ohsawa-Takegoshi extension theorem and applications".
HAYAMA Symposium on Complex Analysis in Several Variables XXIII, Hayama and Tokyo, Japan. Slides.
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2020"Riemann-Roch-Grothendieck theorem for families of curves with hyperbolic cusps and its applications to moduli spaces".
Algebraic and Kähler geometry workshop, Institut Fourier, Saint-Martin-d’Hères, France. Slides.
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2019"Quillen metric for singular families of Riemann surfaces with cusps".
Taipei Conference on Complex Geometry, Academia Sinica, Taipei, Taiwan. Slides.
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2019"Riemann-Roch-Grothendieck theorem for families of curves with hyperbolic cusps and its applications to the moduli space of curves".
Quantization in Symplectic Geometry, Cologne, Germany. Slides.
Seminar talks:
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2023"Submultiplicative norms and filtrations on section rings".
KAAS Seminar, Chalmers University of Technology, Sweden. -
2023"Submultiplicative norms and filtrations on section rings".
Geometric and Functional Analysis Seminar, University of Helsinki, Finland. -
2023"Submultiplicative norms and filtrations on section rings".
Séminaire de Géométrie et Dynamique, Université de Cergy-Pontoise, France. -
2023"Submultiplicative norms and filtrations on section rings".
Seminar of Analysis and Geometry, UPMC, Paris, France. -
2022"On the metric structure of section rings and holomorphic extension theorem".
Séminaires systèmes dynamiques et géométrie, Université d'Angers, France, Slides. -
2022"About extensions of holomorphic jets from submanifolds to ambient manifolds".
Séminaire Géométrie, analyse et dynamique, Université Côte d'Azur, Nice, France, Slides. -
2022"On the metric structure of section rings and holomorphic extension theorem".
Seminario di Algebra & Geometria, Sapienza University of Rome, Italy, Slides. -
2022"Semiclassical Ohsawa-Takegoshi extension theorem and applications".
Informal seminar on complex geometry, Kyoto University, Japan. -
2022"Spanning trees, graph approximations and zeta-regularized determinant of Laplacian".
Rencontre de l’ANR Dimers, Institut Camille Jordan, Lyon, France. Slides. -
2022"Semiclassical Ohsawa-Takegoshi extension theorem".
Seminar of Analysis and Geometry, UPMC, Paris, France. Slides. -
2021"Global analysis on manifolds: discrete and continuous".
Journée de rentrée du CMLS, École Polytechnique, France. Slides. -
2021"Semiclassical Ohsawa-Takegoshi extension theorem".
Séminaire de géométrie, École Polytechnique, CMLS, France. Slides. -
2021"On Monge-Ampère volumes of direct images".
Seminar on Complex Algebraic Geometry and Complex Analysis, in Zoom, joint between Bochum-Essen-Köln-Wuppertal, Germany. Slides. -
2021"On characteristic forms of positive vector bundles, local Kempf-Laksov formula and mixed discriminants".
Seminar on Dirac operators joint with Séminaire d’Analyse et Géométrie, University of Paris-Sud joint with UPMC, France. Slides. -
2021"On Riemann-Roch-Grothendieck theorem for punctured curves with hyperbolic singularities".
Geometry, Number Theory, and Representation Theory Seminar, University of Alberta, Canada. Slides.
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2021"On characteristic forms of positive vector bundles, local Kempf-Laksov formula and mixed discriminants".
Séminaire Analyse Harmonique, University Paris-Sud, France. Slides.
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2020"On characteristic forms of positive vector bundles and mixed discriminants".
Seminar on Complex Geometry, Institut Fourier, Saint-Martin-d'Hères, France.
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2020"Spanning trees, loop measures and zeta-regularized determinants of Laplacian".
The Hypoelliptic Laplacian and NCG Seminar. Slides, Video.
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2020"Spanning trees, loop measures and zeta-regularized determinants of Laplacian on half-translation surfaces".
Théorie spectrale et géométrie, Institut Fourier, Saint-Martin-d'Hères, France. Slides.
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2019"Riemann-Roch-Grothendieck theorem for families of curves with hyperbolic cusps and its applications to the moduli space of curves".
Seminar Differentialgeometrie, Albert Ludwigs University of Freiburg, Freiburg, Germany. Slides.
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2019"Torsion analytique des surfaces cuspidales et ses applications aux espaces de modules", 3 hours.
Seminar on Dirac operators, University of Paris-Sud, Orsay, France. -
2019"Riemann-Roch-Grothendieck theorem for families of surfaces with hyperbolic cusps and its applications to the moduli space of curves", 1.5 hours.
Seminar SAD, University of Cologne, Cologne, Germany. Slides.
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2019"Riemann-Roch-Grothendieck theorem for families of surfaces with hyperbolic cusps and its applications to the moduli space of curves".
Seminar GAAO, Université Clermont Auvergne, Clermont-Ferrand, France. Slides.
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2018"Determinant of Laplacian and Riemann-Roch-Grothendieck theorem with hyperbolic cusps".
Seminar of Analysis and Geometry, UPMC, Paris, France. Slides (in French).
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2018"Riemann-Roch-Grothendieck theorem in the presence of hyperbolic cusps".
Arbre du Noël du GDR GNC, University of Lorraine, Metz, France. Slides.
Short scientific visits:
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2023Scientific visit of Rémi Reboulet and Lars Martin Sektnan, 05/03/2023 - 11/03/2023.
Chalmers University of Technology, Sweden.
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2023Scientific visit of Mikhail Basok and Konstantin Izyurov, 27/02/2023 - 4/03/2023.
University of Helsinki, Finland.
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2022Scientific visit of Laurent Stolovitch, 20/11/2022 - 26/11/2022.
Université Côte d'Azur, Nice, France.
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2022
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2022
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2019Scientific visit of Ken-Ichi Yoshikawa and Ye-Ping Zhang, 16/03/2019 - 24/03/2019.
Kyoto University, Kyoto, Japan.
CV in pdf:
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2016-19PhD in Fundamental mathematics, Université Paris Diderot, Paris 7, France
Title: "On some problems of holomorphic analytic torsion".
Under the supervision of Xiaonan Ma.
Defended on 13.06.2019 in front of the jury: Jean-Michel Bismut, José Ignacio Burgos Gil, Claire Debord, Gerard Freixas i Montplet, Colin Guillarmou, Xiaonan Ma, Peter Zograf. -
2013-16École normale supérieure (Paris) diploma in Fundamental mathematics
École normale supérieure, Paris, France
"Local index theory and analytic torsion". Presentation (in French).
Under the supervision of Xiaonan Ma. -
2014-15Master 2 Fundamental mathematics
Université Paris Diderot, Paris 7, France
"Holomorphic quantification commutes with reduction".
Under the supervision of Xiaonan Ma. -
2013-14Master 1 Mathematics
École normale supérieure, Paris, France
"The Riemannian structure on the set of plane curves".
Under the supervision of Irène Waldspurger.
Teaching:
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2022-23Scientific collaborative project “Gauss-Bonnet"
École polytechnique -
2021-23Introduction to real analysis for 1st year Engineers
École polytechnique -
2021-22Series of Functions, Differential Equations for 2nd year Bachelor students
École polytechnique -
2016-18Linear algebra and analysis for 1st and 2nd year students
Université Paris Diderot, Paris 7