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 JeanPierre 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 AtiyahSinger theorem, local index theory, semiclassical analysis and probability theory.
Currently I'm working on extension problems in complex geometry and their applications.
Publications and preprints:

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 OhsawaTakegoshi extension theorem and asymptotics of the orthogonal Bergman kernel, 72 p.
ArXiv: 2109.06851, 2021. 
On MongeAmpère volumes of direct images,
Int. Math. Res. Not., Vol. 2022, No. 16, pp. 1207212095, 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, cyclerooted spanning forests on discretizations of flat surfaces and analytic torsion,
Math. Z., 301 (4): 32853343, 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): 743751, 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:

On semiclassical OhsawaTakegoshi 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:

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 OhsawaTakegoshi extension theorem and applications".
Complex Geometry and Dynamical Systems, Oberwolfach, Germany. Slides. 
2022"Semiclassical OhsawaTakegoshi extension theorem and applications".
HAYAMA Symposium on Complex Analysis in Several Variables XXIII, Hayama and Tokyo, Japan. Slides.

2020"RiemannRochGrothendieck theorem for families of curves with hyperbolic cusps and its applications to moduli spaces".
Algebraic and Kähler geometry workshop, Institut Fourier, SaintMartind’Hères, France. Slides.

2019"Quillen metric for singular families of Riemann surfaces with cusps".
Taipei Conference on Complex Geometry, Academia Sinica, Taipei, Taiwan. Slides.

2019"RiemannRochGrothendieck 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:

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 CergyPontoise, 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 OhsawaTakegoshi extension theorem and applications".
Informal seminar on complex geometry, Kyoto University, Japan. 
2022"Spanning trees, graph approximations and zetaregularized determinant of Laplacian".
Rencontre de l’ANR Dimers, Institut Camille Jordan, Lyon, France. Slides. 
2022"Semiclassical OhsawaTakegoshi 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 OhsawaTakegoshi extension theorem".
Séminaire de géométrie, École Polytechnique, CMLS, France. Slides. 
2021"On MongeAmpère volumes of direct images".
Seminar on Complex Algebraic Geometry and Complex Analysis,
in Zoom, joint between BochumEssenKölnWuppertal, Germany. Slides. 
2021"On characteristic forms of positive vector bundles, local KempfLaksov formula and mixed discriminants".
Seminar on Dirac operators joint with Séminaire d’Analyse et Géométrie, University of ParisSud joint with UPMC, France. Slides. 
2021"On RiemannRochGrothendieck theorem for punctured curves with hyperbolic singularities".
Geometry, Number Theory, and Representation Theory Seminar, University of Alberta, Canada. Slides.

2021"On characteristic forms of positive vector bundles, local KempfLaksov formula and mixed discriminants".
Séminaire Analyse Harmonique, University ParisSud, France. Slides.

2020"On characteristic forms of positive vector bundles and mixed discriminants".
Seminar on Complex Geometry, Institut Fourier, SaintMartind'Hères, France.

2020"Spanning trees, loop measures and zetaregularized determinants of Laplacian".
The Hypoelliptic Laplacian and NCG Seminar. Slides, Video.

2020"Spanning trees, loop measures and zetaregularized determinants of Laplacian on halftranslation surfaces".
Théorie spectrale et géométrie, Institut Fourier, SaintMartind'Hères, France. Slides.

2019"RiemannRochGrothendieck 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.

2019"Torsion analytique des surfaces cuspidales et ses applications aux espaces de modules", 3 hours.
Seminar on Dirac operators, University of ParisSud, Orsay, France. 
2019"RiemannRochGrothendieck 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.

2019"RiemannRochGrothendieck theorem for families of surfaces with hyperbolic cusps and its applications to the moduli space of curves".
Seminar GAAO, Université Clermont Auvergne, ClermontFerrand, France. Slides.

2018"Determinant of Laplacian and RiemannRochGrothendieck theorem with hyperbolic cusps".
Seminar of Analysis and Geometry, UPMC, Paris, France. Slides (in French).

2018"RiemannRochGrothendieck theorem in the presence of hyperbolic cusps".
Arbre du Noël du GDR GNC, University of Lorraine, Metz, France. Slides.
Short scientific visits:

2023Scientific visit of Rémi Reboulet and Lars Martin Sektnan, 05/03/2023  11/03/2023.
Chalmers University of Technology, Sweden.

2023Scientific visit of Mikhail Basok and Konstantin Izyurov, 27/02/2023  4/03/2023.
University of Helsinki, Finland.

2022Scientific visit of Laurent Stolovitch, 20/11/2022  26/11/2022.
Université Côte d'Azur, Nice, France.

2022

2022

2019Scientific visit of KenIchi Yoshikawa and YePing Zhang, 16/03/2019  24/03/2019.
Kyoto University, Kyoto, Japan.
CV in pdf:

201619PhD 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: JeanMichel Bismut, José Ignacio Burgos Gil, Claire Debord, Gerard Freixas i Montplet, Colin Guillarmou, Xiaonan Ma, Peter Zograf. 
201316École 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. 
201415Master 2 Fundamental mathematics
Université Paris Diderot, Paris 7, France
"Holomorphic quantification commutes with reduction".
Under the supervision of Xiaonan Ma. 
201314Master 1 Mathematics
École normale supérieure, Paris, France
"The Riemannian structure on the set of plane curves".
Under the supervision of Irène Waldspurger.
Teaching:

202223Scientific collaborative project “GaussBonnet"
École polytechnique 
202123Introduction to real analysis for 1st year Engineers
École polytechnique 
202122Series of Functions, Differential Equations for 2nd year Bachelor students
École polytechnique 
201618Linear algebra and analysis for 1st and 2nd year students
Université Paris Diderot, Paris 7