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 focuses on asymptotic problems in complex geometry, while my earlier writings involve topics such as the AtiyahSinger index theorem, local index theory, 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.
Previous positions: From September 2019 to October 2021, I was a postdoctoral researcher at Université Grenoble Alpes, France, working under the direction of JeanPierre Demailly. Prior to that, I was a graduate student at Université Paris Diderot, France, working under the direction of Xiaonan Ma.
Publications and preprints:

Lower bounds on fibered YangMills functionals: generic nefness and semistability of direct images, 20 p.
ArXiv: 2402.08598, 2024. 
Geometry at the infinity of the space of positive metrics: test configurations, geodesic rays and chordal distances, 48 p.
ArXiv: 2305.15300, 2023, to appear in Journal für die reine und angewandte Mathematik. 
The asymptotics of the optimal holomorphic extensions of holomorphic jets along submanifolds
Journal de Mathématiques Pures et Appliquées, Vol. 189, 103586, p. 42, 2024. ArXiv: 2207.02761. 
Complex embeddings, Toeplitz operators and transitivity of optimal holomorphic extensions, 52 p.
ArXiv: 2201.04102, 2022, to appear in Commentarii Mathematici Helvetici. 
Semiclassical OhsawaTakegoshi extension theorem and asymptotics of the orthogonal Bergman kernel,
Journal of Differential Geometry, Vol. 128, No. 2, pp. 639721, 2024. ArXiv: 2109.06851. 
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,
Math. Res. Lett., 30 (6), 1681–1725, 2023. ArXiv: 1911.09087. 
Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem,
Adv. Math., 375, 47 p., 107409, 2020. 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:

Quillen metric theory for surfaces with cusps, 13 p.
2020, Accepted in Actes du séminaire Théorie Spectrale et Géométrie.
Conference talks:

2024"Analytic torsion on Riemann surfaces with hyperbolic cusps", Slides.
Analytic torsion and interactions, Münster, Germany. 
2024

2024"Semiclassical study of Hermitian YangMills functionals".
Pacific Rim Complex and Symplectic Geometry Conference, Daejeon, Korea. 
2024"On the geometry at infinity on the space of Kähler potentials", Slides.
Geometry and Topology Conference, Shanghai, China. 
2024"WessZuminoWitten equation and asymptotic semistabilty of direct images".
Recent progresses in Complex Geometry, NUS, Singapore. 
2024"On the geometry at infinity on the space of Kähler potentials", Slides.
Asymptotics in Complex Geometry. A conference in memory of Steve Zelditch.
Northwestern University, United States. 
2023"On the geometry at infinity on the space of Kähler potentials", Slides.
Taipei Conference on Complex Geometry, Academia Sinica, Taiwan. 
2023"Submultiplicative norms on section rings", Slides, Video, Report.
Recent Developments in Algebraic Geometry, Arithmetic and Dynamics Part 2, NUS, Singapore. 
2023

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:

2024"On HarderNarasimhan slopes of direct images".
New aspects of the theory of Okounkov bodies, École polytechnique, Palaiseau, France. 
2024"WessZuminoWitten equation and asymptotic semistabilty of direct images".
Séminaire de Géométrie et Topologie, Université de Bretagne Occidentale, Brest, France. 
2024A 5lecture minicourse "Local version of the RiemannRochGrothendieck Theorem".
Geometry and Topology Seminar, University of WisconsinMadison, United States. 
2024"Asymptotic study of symmetric powers and normed algebras".
Séminaire d'Analyse Fonctionnelle, Sorbonne Université, Paris, France. 
2024"KobayashiHitchin correspondence for fibrations".
Séminaire de Géométrie Complexe, Institut de mathématiques de Toulouse, France. 
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 WisconsinMadison, United States. 
2023A 3lecture minicourse "Asymptitic problems in complex geodemtry", announcement.
Informal Complex Geometry and PDE Seminar, Columbia University, New York, United States. 
2023"Normes sousmultiplicatives 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 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.
Scientific visits:

2024Scientific visit of Sean T. Paul, 30/03/2024  06/04/2024.
University of Wisconsin Madison, United States.

2023Scientific visit of Tamás Darvas and Richard A. Wentworth, 06/11/2023  10/11/2023.
University of Maryland, United States.

2023Scientific visit of Duong H. Phong, 01/10/2023  30/11/2023.
Columbia University, New York, United States.

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 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: JeanMichel Bismut, José Ignacio Burgos Gil, Claire Debord, Gerard Freixas i Montplet, Colin Guillarmou, Xiaonan Ma, Peter Zograf. 
201316École 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. 
201415Master 2 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.
Undergraduate supervision:
Teaching:

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
Organization:

2024Around Local Index Theory, École polytechnique, France, from 16 to 20 December.