March 23, 2022, in Warsaw together with my daughter, my parents, my two cousins and colleagues-mathematicians from Ukraine. Picture by MichaƂ Kotowski. Here you can find my image at work from times before the Russian Federation started the full scale invasion of my home country.

Masha Vlasenko's Home Page

I am a research fellow at the Institute of Mathematics of the Polish Academy of Sciences in Warsaw (see my page there). In past I was a lecturer at the University College and Trinity College Dublin, and a researcher at the Max Planck Institute in Bonn and Institute of Mathematics in Kyiv.
Contact: masha(dot)vlasenko(at)gmail(dot)com

My interests are in number theory, more particularly in automorphic forms, L-functions, periods and p-adic methods.

I am co-organizing the Warsaw Number Theory Seminar and I am a member of the Co-ordination Committee of the International Centre for Mathematics in Ukraine:

I am also a member of the Board of ASBB Foundation supporting Belarusian and Ukrainian students of mathematics and informatics at the University of Warsaw.

papers and preprints

  • (with Frits Beukers) Frobenius structure and p-adic zeta function [arXiv]
  • (with Bidisha Roy) Frobenius constants for families of elliptic curves [arXiv]
  • (with Frits Beukers) On p-integrality of instanton numbers, Pure and Applied Mathematics Quarterly 19, no. 1, 7--44 (2023) [arXiv]
  • (with Frits Beukers) Dwork crystals III: From Excellent Frobenius Lifts Towards Supercongruences, International Mathematics Research Notices [paper] (open access provided by Dutch Universities and Academic Hospitals)
  • Hodge structures and differential operators, Springer PROMS, volume 373 (2021), 127--139 [arXiv]
  • (with Spencer Bloch) Gamma functions, monodromy and Frobenius constants, Communications in Number Theory and Physics 15 (2021), no. 1, 91--147 [arXiv]
  • (with Frits Beukers) Dwork crystals II, International Mathematics Research Notices 6 (2021), 4427--4444 [paper] (open access provided by Dutch Universities and Academic Hospitals)
  • (with Frits Beukers) Dwork crystals I, International Mathematics Research Notices 12 (2021), 8807--8844 [paper] (open access provided by Dutch Universities and Academic Hospitals)
  • Higher Hasse--Witt matrices, Indagationes Mathematicae 29 (2018), 1411--1424 [arXiv]
  • Formal groups and congruences, Transactions of the AMS 371, no. 2 (2019) 883--902[arXiv]
  • Explicit p-adic unit-root formulas for hypersurfaces [arXiv]
    ideas from this preprint went into the paper ``Higher Hasse--Witt matrices'', see also the extended abstract of my [ talk] at the MATRIX institute
  • (with Anton Mellit) Dwork's congruences for the constant terms of powers of a Laurent polynomial, International Journal of Number Theory, vol. 12, no. 2 (2016), 313 -- 321 [arXiv]
  • (with Vasily Golyshev) Equations D3 and spectral elliptic curves, in `Feynman Amplitudes, Periods and Motives`, Contemporary Mathematics 648 (2015), 135--152 [arXiv]
  • (with Evgeny Shinder) Linear Mahler measures and double L-values of modular forms, Journal of Number Theory 142 (2014), 149--182 [arXiv]
  • (with Don Zagier) Higher Kronecker limit formulas for real quadratic fields, Journal fur die Reine und Angewandte Mathematik 679 (2013), 23--64 [pdf]
  • (with Sander Zwegers) Nahm's conjecture: asymptotic computations and counterexamples, Communications in Number Theory and Physics 5 (2011), 617--642 [arXiv]
  • (with Kevin Hutchinson) Lines crossing a tetrahedron and the Bloch group, in `Contributions to Algebraic Geometry', IMPANGA lecture notes, EMS Series of Congress Reports (2012), 297 -- 304 [arXiv]

popular math talks

2023  Zeta function and algebra (in Ukrainian), open seminar of the Mathematical Society of Chernivtsi
2021  Simple things we don't know: reflections on doing research in number theory, Warsaw Doctoral School Open Day
2019  p-adic continuity, Berkeley Math Circle
2014  p-adic cohomology and counting points on varieties over finite fields, lectures at ICTP in Trieste
2013  Binomial coefficients and p-adic continuity, at UCD MathSoc
2012  Internal geometry of surfaces, at TCD Maths/Physics open day
Apéry's constant and other geometric numbers: towards understanding the motivic Galois group, at UCD/TCD Mathematics Summer School
2006  Complex multiplication [1] and [2], lectures at the Kyiv Institute of Mathematics
My daughter Ivana made this portrait of mine in 2008. Here are her notes of a lecture by Friedrich Hirzebruch from those times.


Number Theory, a course at the Kyiv Academic University (in Ukrainian)

Differential equations and arithmetic, study group at IMPAN

Introduction to Modular Forms, a course at the University of Warsaw

recent and planned scientific visits

2023  April 3, Institut Henri Poincare in Paris, Gilles Christol 80s Birthday workshop
March 27-31, University Lyon 1, workshop Effective Aspects in Diophantine Approximation
March 20-24, Bethe Center Bonn, workshop Geometries and Special Functions for Physics and Mathematics
January 9-11, Institut Henri Poincare in Paris, workshop E-functions, G-functions and Periods
2022  September 19-23, University of Padova, conference Around p-adic cohomologies
July 26 and 28, virtual lectures at Bhaskaracharya Pratishthana in India:
  `Cohomology and congruences' [slides]
  `Calabi-Yau differential operators' [slides]
July 19-22, INI Cambridge, conference Mathematical physics: algebraic cycles, strings and amplitudes
2021  November 8, Warsaw Number Theory Seminar, talk `Integrality of instanton numbers`
April 28, Washington University, (virtual) Algebraic Geometry Seminar
April 27, Univerity of Regensburg, (virtual) SFB colloquium lecture
March 30, University of Versailles - St Quentin, Séminaire différentiel [video]
2020  December 9, Imperial College London, (virtual) talk 'Dwork's congruences and p-adic cohomology'
November 9, Warsaw Number Theory seminar, (virtual) talk 'Dwork crystals'
November 6, GADEPs seminar (IMPA, Rio de Janeiro), (virtual) talk 'Frobenius constants of differential equations'
October 6, University College Dublin, (virtual) talk 'Dwork crystals'
January 8 - February 7, INI Cambridge
2019  December 20, Arithmetic Geometry Seminar at AMU, Poznan
December 9-13, University of Utrecht
November 11-15, p-adic cohomology and arithmetic geometry, Tohoku University
July 15 - 19, school Arithmetic of Connections, Monte Verità
May 13 - 17, conference Transient Transcendence in Transylvania, Brasov
January 20 - May 24, MSRI Berkeley
2018  September 2 - 8, Lukecin, school `Arithmetic of Differential Equations'
September 1 - December 1, Warsaw, program `Varieties: Arithmetic and Transformations`
June 8 - June 15, Ecole de Physique des Houches, talk 'Motivic gamma functions' [notes]
May 28 - June 1, CIRM - Lumini, Algebra, Arithmetic and Combinatorics of Differential and Difference Equations, talk 'Gamma functions, monodromy and Apéry constants' [notes] [video]
March 16, Dutch InterCity Seminar in Utrecht, talk 'Dwork crystals and related congruences'
January 3 - April 20, HIM Bonn, Periods in Number Theory, Algebraic Geometry and Physics, talk 'What is... a motivic gamma function'[notes]
2017   October 1-6, BIRS, p-adic cohomology and arithmetic applications [video]
July 1 - September 30, IHES
June 13-15, Universite Lyon 1 and ENS Lyon, talks 'p-adic unit-root formulas and Dwork cohomology'
January 8-28, Melbourne (Australia), program ` Hypergeometric motives and Calabi--Yau differential equations`
2016   June 28 - July 1, Porquerolles (France), workshop on Automata, Algebraicity and G-functions [slides]
June 20-25, Herstmonceux Castle (East Sussex, UK), Calabi--Yau varieties: arithmetic, geometry and physics
June 1, UAM Poznan, Algebra, geometry and arithmetic seminar [slides]
May 23-28, IMJ-PRG Paris, Arithmetic L-functions and differential geometric methods (Regulators IV)
May 12-14, HU Berlin, Moduli and automorphic forms, talk 'Higher Hasse--Witt matrices'
April 20, University of Gdansk, Geometry Seminar, talk 'p-adic properties of periods'