Finski Siarhei*


Université Paris Diderot, IMJ-PRG
Office: Sophie Germain - 654
8 Place Aurélie Nemours
75013 Paris

Email: siarhei.finski(at)


I am a third year PhD student in pure mathematics in Université Paris Diderot under the direction of Xiaonan Ma.

Research interests:

I am mainly interested in global analysis on manifolds, Atiyah-Singer theorem, local index theory, Riemann surfaces, flat surfaces, moduli spaces, dynamics and L2 invariants.

Recently I also became interested in the spectral behavior of metrized simplicial approximations of a Riemannian manifold when the mesh of the approximation goes to zero.

In my thesis I have studied the properties of holomorphic analytic torsion on complex manifolds. More precisely, I've worked on the analytic torsion on the non-compact surfaces, admitting hyperbolic cusps.

Publications and preprints:

  • Analytic torsion for surfaces with cusps II. Regularity, asymptotics and curvature theorem.
    ArXiv: 1812.11739, 2018.
  • Analytic torsion for surfaces with cusps I. Compact perturbation theorem and anomaly formula.
    ArXiv: 1812.10442, 2018.
  • On the full asymptotics of analytic torsion
    J. Funct. Anal.,  275 (12):  3457 - 3503, ArXiv: 1705.02779, 2018.
  • In progress
    Quillen metric for singular families of Riemann surfaces with cusps.


  • 2018
    "Determinant of Laplacian and Riemann-Roch-Grothendieck theorem with hyperbolic cusps".
    Seminar of Analysis and Geometry, UPMC, Paris, France. Slides (in French).
  • 2018
    "Riemann-Roch-Grothendieck theorem in the presence of hyperbolic cusps".
    Arbre du Noël du GDR GNC, University of Lorraine, Metz, France. Slides.
  • 2017
    "Analytic L2 invariants: Betti numers, Novikov-Shubin-invariants, torsion; classical analytic torsion".
    La Llagonne workgroup on L2 invariants, France. Notes.
  • 2015
    "Hydrodynamics of perfect fluids and diffeomorphism group".
    Working group on infinitely-dimensional manifolds, ENS (Paris), France.
  • 2015
    "Kesten conjecture and a theorem of Varopoulos".
    Working group on random walks on graphs and groups, ENS (Paris), France.
  • 2014
    "Poisson boundary and Dirichlet problem at infinity".
    Working group on random walks on graphs and groups, ENS (Paris), France.

CV in pdf:

  • 2016-19
    PhD in Fundamental mathematics
    Université Paris Diderot, Paris 7, France
    "On some problems of holomorphic analytic torsion".
    Under the supervision of Xiaonan Ma.
  • 2013-16
    École 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.
  • 2014-15
    Master 2 Fundamental mathematics
    Université Paris Diderot, Paris 7, France
    "Holomorphic quantification commutes with reduction".
    Under the supervision of Xiaonan Ma.
  • 2013-14
    Master 1 Mathematics
    École normale supérieure, Paris, France
    "The Riemannian structure on the set of plane curves".
    Under the supervision of Irène Waldspurger.
  • 2010-13
    Bachelor of Science in Applied mathematics and computer science
    Belarusian State University, Minsk, Belarus
    Lie algebras, elementary algebraic geometry.
    Under the supervision of Boris Doubrov.


  • 2016-18
    Linear algebra and analysis for 1st and 2nd year students
    Université Paris Diderot, Paris 7
  • 2010-12
    Lecturer at the National Summer School for Talented Youth
    Naroch, Belarus
  • 2010-12
    Preparing high-school students for mathematical olympiads.
    Author of problems and member of the jury of national mathematical competitions

    Gymnasium 29, Belarus, Minsk
*"Siarhei" is the transliteration of my given name from Belarusian to English. This variant appears in my passport and is the only version used officially. In personal commutications I usually use more common transliteration from Russian, which is "Sergey".