Alexey Ivanovich Zykin
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
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)
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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.