Alexey Zykin Current address: National Research University - Higher School of Economics 117312, Vavilova st., 7 Moscow, Russia Phone: +7 (499) 783 37 84 * 4129 Cell Phone: +7 917 591 34 24 E-mail: alzykin (at) gmail (dot) com

I am currently an associate professor at the Mathematical Department of the Higher School of Economics, the head of the Laboratory of Algebraic Geometry and its applications of HSE and a researcher at the Institute for the Information Transmission problems and Poncelet French-Russian Laboratory

My Curriculum Vitae in English, French and Russian

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).

Publications

• "Asymptotic properties of zeta functions over finite fields", preprint (pdf)
• "Arithmetic, Geometry, Cryptography and Coding Theory" (editor, together with Y. Aubry and C. Ritzenthaler), Contemporary Mathematics, Vol. 574 (2012), 183 pp;
• "On logarithmic derivatives of zeta functions in families of global fields" (with P. Lebacque), International Journal of Number Theory, Vol. 7, Num. 8 (2011), 2139-2156 (arxiv.org)(pdf)
• "Asymptotic methods in number theory and algebraic geometry" (with P. Lebacque), Publications Mathématiques de Besançon, 2011, 47-73;(pdf)
• "Asymptotic properties of Dedekind zeta functions in families of number fields", Journal de Théorie des Nombres de Bordeaux, 22, no. 3 (2010), 689-696 (arxiv.org)(pdf)
• "Jacobians among abelian threefolds: a formula of Klein and a question of Serre" (with G. Lachaud and C. Ritzenthaler), Math. Res. Lett. 17 (2010), no. 2, 323-333(arxiv.org)(pdf)
• "On the Brauer-Siegel theorem for families of elliptic surfaces over finite fields" (in Russian), Mat. Zametki, 86:1 (2009), 148-150 (pdf)
• "On the generalizations of the Brauer-Siegel theorem", proceedings of the Conference AGCT 11 (2007), Contemp. Math. series, 487 (2009), 195-206 (pdf)
• "Brauer-Siegel and Tsfasman-Vladut theorems for almost normal extensions of global fields", Moscow Mathematical Journal, Vol. 5 (2005), Num 4, 961-968 (arxiv.org)(pdf)

Education

• 2006 - 2009: Ph. D, Institut de Mathématiques de Luminy, Université Aix-Marseille II. Thesis: "Propriétés asymptotiques des corps globaux", advisors: Serge Vladuts and Michael A. Tsfasman. The thesis was defended on the 4th of June 2009 in Marseille. Jury: M. Balazard, M. Hindry (referee), G. Lachaud (president), E. Royer, R. Schoof (referee, absent), M. Tsfasman, S. Vladuts.
• 2005 - 2010: Ph. D studies, Mathematical Institute of the Russian Academy of Sciences, Independent University of Moscow. Thesis: "Асимптотические свойства глобальных полей", advisors: Michael A. Tsfasman, Armen G. Sergeev. The thesis was defended on the 14th of October 2010 in Moscow.
• 2001 - 2006: Specialist degree in Mathematics (Master's of Sciences equivalent), Moscow State University, Faculty of Mechanics and Mathematics, advisors: Michael A. Tsfasman, Vasilii A. Iskovskih.
• 2000 - 2005: Specialist degree in Mathematics (Master's of Sciences equivalent), Independent University of Moscow, advisor: Michael A. Tsfasman.
• 1998 - 2001: Moscow Mathematical Highschool number 57.

Conference Talks

• "Arithmetic days in Moscow", Moscow, Russia, June 2011.
  Talk: "Asymptotic properties of zeta functions"
• "Colloque des Jeunes Chercheurs en Théorie des Nombres", Strasbourg, France, June 2010.
  Talk: "Jacobiennes parmi les variétés abéliennes de dimension 3"
• "Théorie des Nombres et Applications",CIRM, Marseille, France, December 2009.
  Talk: "Asymptotic properties of zeta functions"
• "Journées Arithmétiques", Saint-Etienne, France, July 2009.
  Talk: "On the Euler-Kronecker constant and limit zeta functions"
• "Arithmetic, Geometry, Cryptography and Coding Theory", CIRM, Marseille, France, March 2009.
  Talk: "On the asymptotic properties of zeroes of L-functions"
• "Zeta Functions-2", IUM, Poncelet Laboratory, Moscow, Russia, December 2008.
  Talk: "On the Euler-Kronecker constant and limit zeta functions"
• "Arithmetic, Geometry, Cryptography and Coding Theory", CIRM, Marseille, France, November 2007.
  Talk: "On the Brauer-Siegel Theorem for Varieties over Global Fields"
• "Global Fields", IUM, Poncelet Laboratory, Moscow, Russia, July 2007.
  Talk: "Asymptotic problems in the theory of global fields"
• "Zeta Functions", IUM, Poncelet Laboratory, Moscow, Russia, September 2006.
  Talk: "The generalized Brauer-Siegel theorem"
• "Arithmetic, Geometry and Coding Theory", CIRM, Marseille, France, September 2005.
  Talk: "The generalized Brauer-Siegel theorem"

Some seminar Talks

• Number Theory Seminar, Fourier Mathematical Institute, Grenoble, France, June 2012.
  Talk: "Propriétés asymptotiques des fonctions zêta"
• Seminar of the Laboratory of Algebraic Geometry and its Applications, Moscow, Russia, November 2011.
  Talk: "Jacobians and abelian varieties over non algebraically closed fields"
• Seminar of the Moscow Mathematical Society, Moscow, Russia, February 2011.
  Talk: "Asymptotic problems in number theory and limit zeta-functions"
• Seminar of the Institute for Information Transmission Problems, Moscow, Russia, January, 2010.
  Talk: "Asymptotic properties of global fields"
• Algebraic Geometry Seminar, Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia, May 2009.
  Talk: "Jacobians among abelian threefolds"
• Number Theory Seminar, Fourier Mathematical Institute, Grenoble, France, December 2008.
  Talk: "Jacobiennes parmi les variétés abéliennes de genre 3"
• Number Theory Seminar, Hebrew University of Jerusalem, Israel, November 2008.
  Talk: "On the generalized Brauer-Siegel theorem and limit zeta functions"
• Number Theory Seminar, Luminy Mathematical Institute, Marseille, France, November 2007.
  Talk: "Sur le Théorиme de Brauer-Siegel pour les Variétés sur les Corps Globaux"

Other scientific visits

• Scientific visit to the National Center for Theoretic Sciences, Taiwan, July 2011. Invitation by W. Li.
• Scientific visit to the Mathematical Department of Besançon, France, June 2010. Invitation by C. Maire.
• Scientific visit to the Mathematical Laboratory of the Blaise Pascal University, Clermont-Ferrand, France, March 2009. Invitation by E. Royer.
• Winter School "Quantum chaos", Institut de Mathématiques de Bordeaux, France, January 2009.
• Summer School "p-adic Cohomology", Institut für Mathematik, Mainz, Germany, September 2008.
• Summer School "Motives and related topics", Institut des Hautes Etudes Scientifiques, Paris, France, July 2006.
• Summer School "Number fields and curves over finite fields", Anogia, Crete, Greece, July 2005.
• Summer School "Algebraic groups", Georg-August-Universität, Göttingen, Germany, June - July 2005.
• Conference "Gauss-Dirichlet", Georg-August-Universität, Göttingen, Germany, June 2005.
• Exchange "Independent University of Moscow" - "École Normale Supérieure de Paris", Paris, France, January - February 2005.
• Conference "Arithmetic geometry", Euler International Mathematical Institute, St. Petersburg, Russia, June 2004.
• Winter Mathematical School, Weizmann Institute of Science, Rehovot, Israel, January - February, 2004.
• Conference "Arithmetic, Geometry and Coding Theory", CIRM, Marseille, France, May 2003.
• Summer School "Algebraic geometry and information theory", CIRM, Marseille, France, May 2003.

Organized seminars

• Number Theory Seminar (with M. Tsfasman), IUM-Laboratoire Poncelet-IITP, Moscow, 10.2009 - now.
• "Monstrous Moonshine" (with E. Smirnov), Mathematical Departement of HSE, Moscow, 10.2009 - 05.2010.
• "Abelian varieties" (with C. Ritzenthaler), Luminy Mathematical Institute, 10.2008 - 05.2009.
• "Complex multiplication" (with C. Ritzenthaler and D. Kohel), Luminy Mathematical Institute, 11.2007 - 05.2008.
• "Algebraic Surfaces" (with F. Edoukou), Luminy Mathematical Institute, 12.2006 - 05.2007.
• "Automorphic forms" (with W. Zudilin), Moscow State University, 02.2005 - 05.2006.

Teaching experience

• Algebra, Calculus, Geometry, Topology, Discreet Mathematics exercise sessions at the Mathematical Department of HSE, 09.2009 - now.
• Number theory courses at the Mathematical Department of HSE and IUM, 2010 - now.
• Algebraic geometry and commutative algebra exercise sessions, "Math in Moscow" mathematical program for foreign students, IUM, 02.2010 - 05.2010.
• Algebra, Calculus and Number Theory exercise sessions at the IUM, 09.2003 - 05.2008.
• Tutorship in the "Math in Moscow" mathematical program for foreign students, IUM, 09.2005 - 05.2006.

Organized Conferences

• Summer school "Algebra and Geometry" (together with F. Bogomolov, A. Tikhomirov and S. Tikhomirov), Yaroslavl, Russia, July 2012.
• "Arithmetic days" (together with I. Fesenko and I. Zhukov), IUM, Laboratoire Poncelet, Moscow, Russia, April 2012.
• "Global Fields" (together with M. Tsfasman and P. Lebacque), IUM, Laboratoire Poncelet, Moscow, Russia, October 2011.
• Summer school "Algebra and Geometry" (together with M. Verbitsky, A. Tikhomirov and S. Tikhomirov), Yaroslavl, Russia, August 2011.
• "Arithmetic, Geometry, Cryptography and Coding Theory" (together with Y. Aubry and C. Ritzenthaler), CIRM, Marseille, France, March 2011.
• "Zeta Functions-3" (together with M. Tsfasman and M. Balazard), IUM, Laboratoire Poncelet, Moscow, June 2010.
• "Global Fields" (together with M. Tsfasman), IUM, Laboratoire Poncelet, Moscow, July 2008.

Prizes, Awards, Fellowships

• Simons-IUM Fellowship, 2012.
• Moscow Mathematical Society Prize 2011.
• "Dynasty" foundation fellowship, 2011 - 2012.
• Grant of the French Government for a joint French-Russian Ph.D. program, 2006 - 2009.
• Petrovsky Fellowship (IUM), 2004 - 2005.

Reviewer

• Mathematical Reviews, 2010 - now.
• Finite Fields and Applicationsl, 2010 - now.
• Moscow Mathematical Journal, 2009 - now.
• Zentralblatt MATH, 2008 - now.