Alexey Ivanovich Zykin
13 June 1984 — 22 April 2017
Education and Degrees
- 2010
Candidate of Sciences* (PhD) in Mathematical Logic, Algebra and Number Theory
Thesis Title: Asymptotic properties of global fields - 2009
PhD
Thesis Title: Asymptotic properties of global fields - 2005
Degree in Mathematics
Independent University of Moscow, Mathematics
* Candidate of Sciences
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
Research interests
- Zeta-functions and L-functions (modularity, special values, behaviour in families, Brauer--Siegel type results, distribution of zeroes)
- Algebraic geometry over finite fields (points on curves and varieties over finite fields, zeta functions, relations to coding theory)
- Families of fields and varieties, asymptotic theory (infinite number fields and function fields, limit zeta-functions)
- Abelian varieties and Elliptic Curves (Jacobians among abelian varieties, families of abelian varieties over global fields)
Young Faculty Support Programme (Group of Young Academic Professionals)
Category "Future Professoriate" (2013)
Moscow Mathematical Society Prize for young mathematicians (2011)
Pierre Deligne – “Dynasty” Foundation Fellowship (2011-2013)
Simons–IUM Fellowship (2012, 2013)
Publications14
- Article Zykin A. I., Ballet S. Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields // Designs, Codes and Cryptography. 2019. Vol. 87. P. 517-525. doi
- Preprint Ballet S., Zykin A. I. Dense families of modular curves, prime numbers and uniform symmetric tensor rank of multiplication in certain finite fields / Cornell University. Series arXiv "math". 2017.
- Preprint Lebacque P., Zykin A. I. On M-functions associated with modular forms / Le Centre pour la Communication Scientifique Directe. Series HAL "HAL:archives-ouvertes". 2017.
- Article Zykin A. I. Asymptotic properties of zeta functions over finite fields // Finite Fields and Their Applications. 2015. Vol. 35. P. 247-283. doi
- Article Lebacque P., Zykin A. I. On the Number of Rational Points of Jacobians over Finite Fields // Acta Arithmetica. 2015. Vol. 169. No. 4. P. 373-384. doi
- Article Zykin A. I. Uniform distribution of zeroes of L-functions of modular forms // Contemporary Mathematics Series. 2015. Vol. 637. P. 295-299.
- Book Arithmetic, Geometry, Cryptography and Coding Theory (2012) / Ed. by A. I. Zykin, Y. Aubry, C. Ritzenthaler. Issue 574. Providence : American Mathematical Society, 2012.
- Article Zykin A. I., Lebacque P. Asymptotic methods in number theory and algebraic geometry // Publications Mathematiques de Besancon. 2011. P. 47-73.
- Article Zykin A. I., Lebacque P. On logarithmic derivatives of zeta functions in families of global fields // International Journal of Number Theory. 2011. Vol. 7. No. 8. P. 2139-2156.
- Article Zykin A. I. Asymptotic properties of Dedekind zeta functions in families of number fields // Journal de Theorie des Nombres de Bordeaux. 2010. No. 22(3). P. 689-696.
- Article Zykin A. I., Ritzenthaler C., Lachaud G. Jacobians among abelian threefolds: a formula of Klein and a question of Serre // Mathematical Research Letters. 2010. Vol. 17. No. 2. P. 323-333.
- Chapter Zykin A. I. On the generalizations of the Brauer-Siegel theorem, in: Arithmetic, Geometry, Cryptography and Coding Theory (2009) / Ed. by G. Lachaud, C. Ritzenthaler, M. A. Tsfasman. Providence : American Mathematical Society, 2009. P. 195-206.
- Article Зыкин А. И. Теорема Брауэра-Зигеля для семейств эллиптических поверхностей над конечными полями // Математические заметки. 2009. Т. 86. № 1. С. 148-150.
- Article Zykin A. I. Brauer-Siegel and Tsfasman-Vladut theorems for almost normal extensions of global fields // Moscow Mathematical Journal. 2005. Vol. 5. No. 4. P. 961-968.
