Alexey Zaytsev personal website

Welcome to my web site

My name is Alexey Zaytsev, I am a founder of the online-project 01Math.com

Academic positions
Academic positions
My Research Interests
Degree
Fellowships and Honors
Publications
Teaching Experience
Conferences and Workshops
Recent Talks
Conferences organizer
Reviewer
Referees

Academic positions

1998 - 2001 Lecturer
Baltic State Academy
2001 - 2003 Lecturer
Baltic State Academy
2003 - 2008 Phd student under supervision by Prof. Gerard van der Geer
University of Amsterdam
2008 - 2011 Postdoctoral position research host Prof. Gary McGuire
University College Dublin and Claude Shannon Institute
2011 - 2017 Head of laboratory "mathematical methods in information theory"
Immanuel Kant Baltic Federal University
2017 - 2020 Head of department of mathematics
International Gymnasium in Skolkovo
2017 - 2020 Leading research scientist
SkolTech

My Research Interests

Algebraic Geometry (with emphasis on function fields, algebraic curves over finite fields), Abelian Varieties over Finite fields, Elliptic Curves, Number Theory, Coding Theory and Cryptography, Groups Schemes, Deformation Theory of Abelian Varieties, the Zeta Functions of Towers of Function Fields

Degree

1998 Master Degree in Mathematics
Kaliningrad State University (Russian Federation)
2008 Ph. Degree
Universiteit van Amsterdam (the Netherlands)

Fellowships and Honors

1999-2000 Leonhard Euler Scholarship program (as most promissing young reseacher)
2002 Certificate from Russian Academy of Sciences for high level of supervision of young scientists
2003-2007 Research grant from Netherlands Organization for Scientific (N.W.O.)
2008- 2011 Postdoctoral fellowship at University College Dublin
Short Term Travel Fellowship, 07/RFP/MATF846 STTF09 from Science Foundation of Ireland
Grant for creating a master program in mathematics in Kant Baltic Federal University

Publications

1998 Non-abelian Kummer extenstions
proceedings of Kaliningrad State University
2001 Generators of Galois closure of a sequence of curves attaining the Drinfeld-Vladut bound
journal "Differential geometry of manifolds of figures" (Kaliningrad State University, 2001) (joint work with S. Aleshnikov)
2002 Coding theory and Galois closure of optimal tower
proceedings of Baltic State Academy, Kalinigrad
2002 "The Galois closure of tower of function fields that attains the Drinfeld-Vladut bound" А. Зайцев; A. Zaitsev
Доклады международного математического семинара к 140-летию со дня рождения Давида Гильберта из Кенигсберга и 25-летию математического факультета. -Калининград, 2002.-С.223-227 (Proceedings of International mathematical seminar dedicating to David Hilbert and the 25th anniversary of the faculty of mathematics of KSU)
2003 Some results on Galois closure
Collection of scientific works of XXV conference of young scientists (MechMat, Moscow State University, 2003)
2005 Galois closure of the Garcia-Stichtenoth tower
журнал "Finite Fields and Their Applications", 2007, volume 13, pp.751-761 (появилась в arxiv в 2005 году, http://arxiv.org/abs/math/0504431)
Optimal curves of low genus over finite fields
2008 Optimality properties of curves over finite fields
диссертация (Pdh thesis) pdf
2010 Оптимальные кривые рода 3 над конечными полями с дискриминантом -19
Прикладная и Дискретная Математика, Томский государственный университет, SIBECRYPT'10 (в соатворстве с Е.С. Алексеенко и С.И. Алешников)
2011 Optimal Curves of Genus 3 over Finite Fields with Discriminant -19
journal "Finite Fields and Their Applications", 2011, volume 17, pp.350-358, (joint work with K. Alekseenko, S. Aleshnikon and N. Markin)
2010 On the Zeta Functions of an optimal tower of function fields over $\\F_4$
Finite fields: theory and applications, pp. 327-338, Contemp. Math., 518, Amer. Math. Soc., Providence, RI, 2010, (joint work with G. McGuire)
2012 The Number of Rational Points On Genus 4 Hyperelliptic Supersingular Curves in Characteristic 2
(joint work with G. McGuire) "Finite Fields and Their Applications", Volume 18, Issue 5, September 2012, pages 886-893
2014 Classification of characteristic polynomials of simple supersingular abelian varieties over finite fields
Functiones et Approximatio, Volume 51, Number 2 (2014), 415-436. (joint work with V.Singh and G. McGuire)
2013 Generalization of Deuring Reduction Theorem
(http://arxiv.org/abs/1209.5207) Volume 392, 15 October 2013, Pages 97-114 "Journal of Algebra"
2014 An improvement of the Hasse-Weil-Serre bound for curves over some finite fields
"Finite Fields and Their Applications", Volume 30 November 2014, Pages 88-99
2015 Explicit equations of optimal curves of genus 3 over certain finite fields with three parameters
"Algorithmic Arithmetic, Geometry, and Coding Theory: 14th International Conference on Arithmetic, Geometry, and Coding Theory", 2015, CIRM, Marseille, France, Pages 319-325 (joint work with Ekaterina Alekseenko)
2016 Optimal curves of low genus over finite fields
"Finite Fields and Their Applications" Volume 37, January 2016, Pages 203-224
2018 Computing algorithm for reduction type of CM abelian varieties
https://arxiv.org/abs/1809.10368

Teaching Experience

1999 - 2000 Instructor of a course "Calculus"
Baltic State Academy
2000 - 2001 Instructor of courses "Calculus" and "Probability theory"
Baltic State Academy
2001 - 2002 Instructor of courses "Calculus" and "Probability theory".
Baltic State Academy
2002 - 2003 Lecturer and Instructor of a course "Introduction to the theory of Elliptic Curves"
Kaliningrad State University
2002 - 2003 Lecturer of a course "Discrete Mathematics"
Baltic State Academy
2005 - 2006 Instructor of a course "Algebra II"
University van Amsterdam
2008 - 2009 Seminar: Elliptic curves and Cryptography
Claude Shannon Institute
2009 - 2010 Lecturer and Instructor of a course "Vector Spaces and Coding".
University College Dublin
2010 - 2011 Seminar: "An elementary proof of the Hasse-Weil bound"
Claude Shannon Institute
2011 - 2012 Seminar "Arithmetic geometry, Cryptoraphy and Coding Theory"
Immanuel Kant Baltic Federal University
2011 - 2012 a course "Equations over finite fields"
Higher School of Economics Faculty of Mathematics
2011 - 2012 a course "Group Schemes"
Independent University of Moscow
2011 - 2012 Lecturer and Instructor of a course "Probability theory and mathematical statistics"
Immanuel Kant Baltic Federal University
2012 - 2013 Lecturer and Instructor of a course " Methods and Algorithms of generation hyperelliptic curves in cryptography"
Immanuel Kant Baltic Federal University

Conferences and Workshops

March 25-129, 2009 ESF Workshop on Codes, Cryptography and Coding Theory Institut de Mathématiques de Luminy
30th March - 3rd April, 2009 AGCT-12 CIRM Luminy, Marseille, France
September 22-24 The 12th Workshop on Elliptic Curve Cryptography Utrecht, the Netherlands
May 2009 The Claude Shannon Institute Workshop on Coding and Cryptography Cork
July 2009 Fq9 International Conference on Finite Fields and their Applications Dublin, Ireland
May 2010 The Claude Shannon Institute Workshop on Coding and Cryptography Cork
June 2010 Conference "Zeta Functions" Laboratoire CNRS J.-V. Poncelet and Independent University of Moscow
September, 2010 Geometry and Arithmetic Schiermonnikoog
November, 2010 RISC/Intercity number theory seminar on Crypto, Coding and Geometry
May, 2011 The Irish Geometry Conference
May, 2011 The Claude Shannon Workshop on Coding and Cryptography, Cork
October, 2011 Global Fields Laboratoire CNRS J.-V. Poncelet and Independent University of Moscow
April, 2012 Arithmetic Days Laboratory of Algebraic Geometry and its Applications , Mathematical Department of the National University Higher School of Economics and Laboratoire CNRS J.-V. Poncelet, Moscow
November, 2012 "Zeta functions" the 4th conference of zeta functions Laboratory of Algebraic Geometry and its Applications, Mathematical Department of the National University Higher School of Economics and Laboratoire CNRS J.-V. Poncelet, Moscow
May, 2013 Conference "Diophantine Geometry" University of Paris 7, Laboratoire Poncelet, Institute for Information Transmission Problems, State University Higher School of Economics, Moscow, Russia,
May, 2013 Arithmetic days 2013 St.Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia
June, 2013 Arithmetic, Geometry, Coding Theory and Cryptography 14 Marseille, Luminy, France
November 11-15, 2013 Algebraic curves over finite fields
June 2014 Algebraic Geometry and Number Theory on the occasion of M.A. Tsfasman's and S.G. Vladuts' 60th birthday, Independent University of Moscow, Laboratoire Poncelet, Moscow, Russia
December 1-5, 2014 Zeta functions 5 Independent University of Moscow, Laboratoire Poncelet, Moscow, Russia
June 10-14, 2019 Arythmeic, Geometry, Cryptography and Coding Theory (17th Edition) CIRM, Люмини, Марсель, Франция

Recent Talks

October 2008 Curves with many rational points
UCD, Algebra seminar
May, 2009 Explicit equations of optimal curves genus 3
CSI Workshop on Coding and Cryptography
July 2009 On the Zeta Functions of an optimal tower of function fields over $\F_4$
Fq9
2010 The Galois closure of a tower of function fields
UCD, Algebra Seminar
June 2010 The Number of Rational Points On Genus 4 Hyperelliptic Supersingular Curves in Characteristic 2"
Conference "Zeta Functions", Moscow
January 2011 Curves over finite fields with many rational points, existence and constructions
Nanyang Technological University, Singapore
April, 2011 Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes
UCD, Dublin
2011 Curves over finite fields with many rational points, existence and constructions"
video conference with Telecom ParisTech, April
May, 2011 Reduction of abelian varieties with complex multiplication and its first truncated Barsotti-Tate group schemes
The Irish Geometry Conference, Galway
June, 2011 Zeta functions and Towers of Function Fields over Finite Fields
HSE, Faculty of Mathematics
June, 2011 Introduction into the theory of Abelian varieties
Kant BFU, Faculty of Mathematics
October, 2011 Abelian varieties with complex multiplication and their first truncated Barsotti-Tate group schemes
IMU
April, 2012 Towers of function fields over finite fields and their sequences of zeta-functions
IMU
June 2012 Existence and constructions of curves over finite fields with many rational points
Institute of Mathematics Szczecin University
June 2012 Abelian varieties with complex multicplication and their first truncated Barsotti-Tate group schemes
Institute of Mathematics Szczecin University
November 2012 Generalization of Deuring reduction theorem"
April 2013 Generalization of Deuring Reduction Theorem
Adam Mickiewicz University in Poznan (Poland)
Май, 2013 Canonical coordinates on the canonical lift via Dieudonne modules
conference "Diophantine Geometry", Москва, Россия
May, 2013 Generalization of Deuring Reduction Theorem
conference "Arithmetic days 2013", St.Petersburg Department of Steklov Mathematical Institute, St. Petersburg, Russia
November, 2013 Zeta functions of towers of function fields
workshop2 "Algebraic curves over finite fields", Austria, Linz, RICAM
December, 2014 Coefficients of Zeta functions of the second Garcia-Stichtenoth tower as polynomial functions
conference "Zeta functions 5", Moscow, Russia
April, 2017 The degree of exetension of the Galois closure of a tower of function felds and Chebotarev density theorem
Conference \"Algebra and number theory in Kaliningrad\", Kaliningrad
March 2018 01Math.com online project as a basis for mathematical studies in middle school and modern digital environment
Seminar for teachers in MCCME, Moscow
September 2018 Graphs and Zeta functions of optimal towers of function fields over finite fields
Sixteenth International Workshop on Algebraic and Combinatorial Coding Theory, Kaliningrad, Svetlogorsk

Conferences organizer

June, 3-7, 2013 AGCT14
Luminy, Marseille, France (together with Stéphane Ballet and Marc Perret)
September, 1-7, 2013 ITaS
Kaliningrad, Russia (BFU Local Organizing Committee)

Reviewer

Referees

Professor Gary McGuire

Claude Shannon Institute University College Dublin School of Mathematical Sciences

e-mail: gary.mcguire AT ucd.ie
Professor Gerard van der Geer

Korteweg-de Vries Instituut Universiteit van Amsterdam

e-mail: geer at science.uva.nl
Michael A. Tsfasman

Institut de Mathematiques de Luminy Independent University of Moscow

e-mail: tsfasman AT iml.univ-mrs.fr
Professor Henning Stichtenoth

Sabanci University - FENS

e-mail: henning AT sabanciuniv.edu
Grigory Kabatyansky

Skolkovo Institute of Science and Technology

e-mail: G.Kabatyansky AT skoltech.ru