## Masha VlasenkoI am an associate professor 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 Dublin 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)comMy interests are in algebraic number theory, more particularly in automorphic forms, L-functions, periods and p-adic methods. I am co-organizing the Warsaw Number Theory Seminar. I am a member of the Co-ordination Committee of the International Centre for Mathematics in Ukraine (ICMU) and a member of the Board of ASBB Foundation supporting Belarusian and Ukrainian students of mathematics and informatics at the University of Warsaw. |
23 March 2022, in Warsaw together with my younger daughter, my parents, my two cousins and colleagues-mathematicians from Ukraine. Picture by Michał Kotowski. Here is my image at work from times before the Russian Federation started the full scale invasion of our home country.
Voices from the Bombed Universities of Ukraine (with Efim Zelmanov), Notices of the American Mathematical Society, June/July 2023 - an interview with Oksana Bezushchak, Sergey Gefter and Volodymyr Kadets When Scientists Become Political Dissenters (with Ahmed Abbes, Michel Broué, Chandler Davis, Adrien Deloro, Ivar Ekeland and Michael Harris), Scientific American, 16 October 2020 |

- (with Frits Beukers) Frobenius structure and p-adic zeta function [arXiv]
- (with Bidisha Roy) Frobenius constants for families of elliptic curves, The Quarterly Journal of Mathematics, 74, issue 4 (2023), 1571–1595 [paper] (open access provided by Polish Institutions - ICM Consortium)
- (with Frits Beukers) On p-integrality of instanton numbers, Pure and Applied Mathematics Quarterly 19, no. 1, 7–44 (2023) – volume dedicated to Don Zagier's 70th birthday [paper]
- (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]
- (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]

2024 | Invisible holes in diophantine equations (in Polish), a lecture for high schoolers at the 9th Congress of Young Mathematicians in Wrocław |

Congruences and cohomology, notes of lectures given at ICTP Summer School "Number Theory and Physics" and the Brazilian Algebra Meeting at IME-USP in São Paulo. Based on a series of joint papers with Beukers. Video records of ICTP lectures: [1][2][3] | |

Numbers, shapes and ideas (in Ukrainian), public lecture at the inaugugartion of ICMU working space in Kyiv | |

2023 | Varieties in the mirror and arithmetic (in Polish), 66 School of Illustrative Mathematics, Siedlce |

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 Bonn in 2008.
Here are her notes of a lecture by Friedrich Hirzebruch from those times. |

p-adic modular forms, study group at IMPAN, 2023/24

Number theory, a course at the Kyiv Academic University (in Ukrainian), 2023

Differential equations and arithmetic, study group at IMPAN, 2021/22

Introduction to modular forms, a course at the University of Warsaw, 2020 and 2022

Sebastian Gontarek, MSc thesis `p-adic modular forms', University of Wrocław 2024

Mieszko Zimny, MSc thesis `Dwork's congruences and zeta functions`, University of Warsaw 2023

Semen Słobodianiuk, BSc thesis 'Integral ratios of factorials and algebraic hypergeometric functions', University of Warsaw 2022

Ewan Dalby, BSc thesis / final year project `Congruences for the Fourier coefficients of modular forms', Trinity College Dublin 2015

Jack Kelly, BSc thesis / final year project `Algebraic hypergeometric functions', Trinity College Dublin 2013

David Mulligan, BSc thesis / final year project `The Weil Conjectures for Elliptic Curves', Trinity College Dublin 2013

2024 | October 7-19, University of Vienna, workshop Algebraicity and Transcendence for Singular Differential Equations |

September 23, Chernivtsi University, Hans Hahn memorial conference | |

September 1-6, Mathematical Research Institute in Oberwolfach, workshop Explicit Methods in Number Theory | |

July 22-27, Nisyros island in Greece, conference Periods in algebraic geometry and automorphic forms | |

June 17-21, ICTP Trieste, School on Number Theory and Physics | |

July 15-19, IME-USP in in São Paulo, 27th Brazilian Algebra Meeting | |

April 22-26, HIM Bonn, follow-up-workshop for the Trimester Programme Periods in Physics, Number Theory and Algebraic Geometry | |

2023 | October 6, University of North Carolina, Physically inspired mathematics seminar, remote lecture `Calabi-
Yau differential operators' |

April 3, Institut Henri Poincare in Paris, Gilles Christol 80s Birthday workshop, lecture`Frobenius structure and p-adic zeta function` | |

August 7-11, ICMU in Kyiv, organising school and conference Numbers in the Universe: Recent Advances in Number Theory and Its Applications | |

March 27-31, University Lyon 1, workshop Effective Aspects in Diophantine Approximation, lecture `Frobenius structure and p-adic zeta function` | |

March 20-24, Bethe Center Bonn, workshop Geometries and Special Functions for Physics and Mathematics, lecture 'Calabi-Yau Operators and p-adic zeta function' | |

January 9-11, Institut Henri Poincare in Paris, workshop E-functions, G-functions and Periods, lecture 'Integrality of instanton numbers' | |

2022 | November 1-5, ICTP Trieste |

September 19-23, University of Padova, conference Around p-adic cohomologies, lecture 'Cohomology and congruences' | |

July 26 and 28, remote 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, remote lecture in the Algebraic Geometry Seminar | |

April 27, Univerity of Regensburg, remote SFB Colloquium lecture | |

March 30, University of Versailles - St Quentin, Séminaire différentiel [video] | |