Contact:
École Polytechnique,
CMLS, Office: 06.1006
Email: finski.siarhei(at)gmail.com
siarhei.finski(at)polytechnique.edu
I am a mathematician working in geometry.
Research interests: Global analysis on manifolds and complex geometry. My most recent work deals with asymptotic problems in complex geometry; some of my previous writings are related to the Atiyah-Singer index theorem, local index theory, semi-classical analysis, pluripotential theory and probability theory.
Current position: Researcher (chargé de recherche) in CNRS. Professeur chargé de cours d’exercice incomplet, Centre de mathématiques Laurent Schwartz, École Polytechnique, Palaiseau, France. From October to November 2023, I’m visiting Columbia University, New York.
Previous positions: From September 2019 to October 2021, I was a postdoctoral researcher at Université Grenoble Alpes, France, working under the direction of Jean-Pierre Demailly. Prior to that, I was a graduate student at Université Paris Diderot, France, working under the direction of Xiaonan Ma.
Publications and preprints:
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Geometry at the infinity of the space of positive metrics: test configurations, geodesic rays and chordal distances, 48 p.
ArXiv: 2305.15300, 2023. -
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, to appear in Journal of Differential Geometry. -
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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On semiclassical Ohsawa-Takegoshi extension theorem, 24 p.
2022, submitted to proceedings of HAYAMA Symposium on Complex Analysis in Several Variables XXIII. -
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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2023"Submultiplicative norms on section rings", Slides, Video, Report.
Recent Developments in Algebraic Geometry, Arithmetic and Dynamics Part 2, Singapore. -
2023
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2023"Geometry at the infinity of the space of positive metrics".
SCV, CR geometry and Dynamics, Université Côte d'Azur, Nice, France. -
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"On the geometry at infinity on the space of Kahler potentials and submultiplicative filtrations".
Informal Geometric Analysis Seminar, University of Maryland, United States. -
2023"Asymptotic study of filtrations on section rings and geodesic rays of metrics".
Geometry and Topology Seminar, University of Wisconsin-Madison, United States. -
2023A 3-lecture minicourse "Asymptitic problems in complex geodemtry", announcement.
Informal Complex Geometry and PDE Seminar, Columbia University, New York, United States. -
2023"Normes sous-multiplicatives sur les anneaux de sections".
Séminaire de géométrie de l'École polytechnique, Palaiseau, France. -
2023"Filtrations on section rings and geometry of the space of Kähler metrics".
Seminire Algèbre et géométries, Institut Fourier, Gières, France. -
2023"Asymptotic study of filtrations on section rings and geodesic rays of metrics".
Seminar for trimester "Higher structures in Enumerative Geometry", Institut Henri Poincaré, Paris, France. -
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 mathematics, Université Paris Diderot, Paris 7, France
Title: "On some problems of holomorphic analytic torsion", pdf, slides.
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 mathematics
École normale supérieure, Paris, France
"Local index theory and analytic torsion". Presentation (in French).
Under the supervision of Xiaonan Ma. -
2014-15Master 2 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.
Undergraduate supervision:
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2022-23Master 1 thesis: Gauss-Bonnet theorem, Glaib Ilyas, Kobilinsky Léonard, Lee Jhe-Han, Vanheeghe Vivian, Ward Benjamin, thesis (in French).