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 before that I was a researcher at the Max Planck Institute in Bonn and Institute of Mathematics in Kyiv.

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

I can be contacted at masha dot vlasenko at gmail dot com


My daughter Ivana made this portrait of mine in 2008. Here are her notes of a lecture by Friedrich Hirzebruch from those times. In case you are interested to see my actual image, here is a photograph (courtesy of Piotr Achinger).
   


recent preprints and papers

  • Formal groups and congruences [arXiv]
  • Explicit p-adic unit-root formulas for hypersurfaces [arXiv]
  • (with Anton Mellit) Dwork's congruences for the constant terms of powers of a Laurent polynomial, International Journal of Number Theory, 2016 [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]
  • Generalization of the Stark unit for abelian L-functions with multiple zeros [arXiv]

scientific visits and talks

2016   June 20-25, Herstmonceux Castle (East Sussex, UK), Calabi-Yau varieties: arithmetic, geometry and physics
June 1, UAM Poznan, Algebra, geometry and arithmetic seminar
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'
2015   November 24, University of Mainz, SFB Colloquium, talk 'Arithmetic properties of coefficients of logarithms of formal group laws'
November 10, Institute of Mathematics in Kyiv, Algebra Seminar, talk 'Arithmetic properties of formal groups'
October 23, IMPANGA, Warsaw
July 5-11, Oberwolfach, Explicit methods in number theory, talk 'Formal groups and congruences'
February 16-20, CRM of Montréal, Regulators, Mahler measures, and special values of L-functions, talk 'Explicit p-adic unit-root formulas for hypersurfaces'
January 14, MPIM Bonn, Seminar on recurrences and L-values
2014  November 10, University of Warwick, Number Theory Seminar, talk 'Dwork's congruences for periods of families of Calabi-Yau hypersurfaces'
September 1-12, ICTP Trieste, L-functions and modular forms
    Notes of my course on Monski-Washnitzer cohomology and Kedlaya's algorithm for counting points on hyperelliptic curves over finite fields
August 18 - 22, MSRI Berkeley, New Geometric Methods in Number Theory
June 23-27, IHES Bures-sur-Yvette, Algebra, Geometry and Physics
April 3, Dublin Area Mathematics Colloquium, talk 'Counting points over finite fields on Calabi-Yau hypersurfaces'
March 29, UCD Algebra and Number Theory Seminar, talk 'Congruences for the constant terms of powers of a Laurent polynomial'
2013  July 14-20, Oberwolfach, Explicit methods in number theory, talk 'Determinantal differential operators with Frobenius structure'
July 10-12, Utrecht, Special functions and special numbers
June 15-20, Saariselkä, Arctic Number Theory Workshop, talk 'Dwork's congruences and p-adic overconvergence'
March 11-14, Dublin, 27th Automorphic Forms Workshop [slides]
2012  December 15-21, Bonn, Galois representations and pencils of Calabi-Yau motives, talk 'D3 equations and spectral elliptic curves'
November 5-9, Paris, Hypergeometric motives
August 26 - September 1, Oberwolfach, Low-dimensional topology and number theory
July 2-6, ICMAT Madrid, Periods and motives: a modern perspective on renormalization [slides]
June 25-29, ICTP Trieste, Hypergeometric motives
June 13-14, Irish Geometry Conference, University College Cork, talk 'Geometricity problem for differential equations'
May 29 - June 1, Paris, Hypergeometric series and their generalizations in algebra, geometry, number theory and physics, talk 'Mahler's measure of a linear form and double L-values'
April 5, Dublin, K-Theory, Quadratic Forms and Number Theory seminar at UCD
March 23-28, MPIM Bonn, Motivic structures on quantum cohomology
February 27 - March 1, Cologne, Modular forms, mock theta functions, and applications [slides]
2011  July 17 - July 23, 2011, Oberwolfach, Explicit methods in number theory [slides]


popular math talks

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
Apery's constant and other geometric numbers: towards understanding the motivic Galois group, at UCD/TCD Mathematics Summer School


teaching

Trinity College Dublin

Introduction to Number Theory (an older version of this course is here)
Introduction to Modular Forms
Lebesgue integral

University College Dublin

Modular Forms of One Variable (graduate level)

undergraduate research projects

2015  Seán Mac DhonnagáinCongruences for the coefficients of powers of a polynomial
2014  Ewan DalbyCongruences for the Fourier coefficients of modular forms
2013  Adam Keilthy, Owen Ward
and Jack Geary
Integral ratios of factorials
David MulliganWeil conjectures for elliptic curves
Jack KellyAlgebraic hypergeometric functions
2012  Modular parametrization of families of elliptic curves  
Eoin Ó MurchadhaGeneralizing Menelaus' theorem to algebraic curves paper
Aran Nolan, Padraig Condon
and Ewan Dalby
Extremal Laurent polynomials in two dimensions description and students' report on the results
Undergraduate number theory study group
2011  Una Eilis Ni Eigeartaigh    Ramified coverings of the Riemann sphere

Mathematical battle UCD vs TCD:   [problems] [rules] [photo report]

service courses

Linear algebra (for engineeers)
Multivariable calculus (for engineers)
Graphs and networks