Sergey Tikhonov

Centre de Recerca Matemàtica

Experimental Sciences & Mathematics

I was born in Russia in 1976. I graduated from the Lomonosov Moscow State University in 1999 and obtained my PhD in Mathematics from MSU in 2003. 2004-2006: Marie Curie Fellow at the Centre de Recerca Matemàtica, Barcelona. 2006-2008: Post-doctoral Fellow at the Scuola Normale Superiore, Pisa. 2008-September 2012: ICREA Researcher, CRM From September 2012, I am an ICREA Research Professor at the Centre de Recerca Matemàtica. 2009: ISAAC Award. 2013: Humboldt Research Fellowship for Experienced Researchers.

Research interests

Mostly my research deals with Fourier Analysis and Approximation Theory. Particularly, I study the relationship between “smoothness” of a function and the possibility to approximate or to represent this function by a sum of “simple” functions. The case when “simple” functions have wave structure is of special interest.

Selected publications

– Bondarenko A & Tikhonov S 2017, ‘Bernstein inequalities with nondoubling weights‘, J. Eur. Math. Soc., vol. 19, no. 1, pp 67-106.
– Ganzburg MI & Tikhonov SY 2017, ‘On Sharp Constants in Bernstein–Nikolskii Inequalities’, Constructive Approximation, vol. 45,  pp 449–466.
– Temlyakov V & Tikhonov S 2017, ‘Remez-Type Inequalities for the Hyperbolic Cross Polynomials’, Constr. Approx., vol. 46, pp 593-615.
– De Carli L,  Gorbachev  D &  Tikhonov S 2017 ‘Pitt inequalities and restriction theorems for the Fourier transform‘, Revista Matem. Iberoamericana, 33, no. 3,  pp 789-808.

Selected research activities

Research Visits:
Research in teams, BIRS (Canada).
Invited Researcher at University of Alberta (Canada); Laboratoire Jacques-Louis Lions, Universite Pierre et Marie Curie, Paris (France); and IHES, Bures-sur-Yvette (France).

Invited Conference Talks:

New perspectives in the theory of function spaces and their applications (Poland); Workshop on Fourier Analysis and Related Fields, (Hungary); International Conference in Approximation Theory, (USA); AMS Sectional Meeting, Hunter College, New York (USA); and Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis (Russia).

Seminar and Colloquium Talks:

PIMA/AMI Seminar, Univ. of Alberta, Edmonton (Canada); Approximation Theory Seminar, Univ. of Alberta, Edmonton (Canada); General Seminar, USC, SC (USA); Analysis Seminar, Aristotle University of Thessaloniki (Greece); Approximation Theory Seminar, Steklov Math. Inst, Moscow (Russia); and Analysis Seminar, Univ. of Coimbra (Portugal).

Member of Editorial board:

Abstract and Applied Analysis, Analysis Mathematica, Bulletin of Mathematical Analysis and Applications, Demonstratio Mathematica, Jaen Journal on Approximation, Journal of Mathematical Analysis and Applications, Guest editor of the special issue “Function Spaces and Approximation Theory”, Analysis Math., V. 43, Is. 2, 2017.

Conference Organizer:

June 26-30, 2017: Main organizer of the Follow up  Workshop on Approximation Theory and Function Spaces,  Barcelona (Spain).