Sergey Tikhonov

Sergey Tikhonov

Centre de Recerca Matemàtica

Experimental Sciences & Mathematics

I graduated from the Lomonosov Moscow State University in 1999 and obtained the PhD degree in Mathematics from MSU in 2003. From September 2012, I am an ICREA Research Professor at the Centre de Recerca Matemàtica.

  • 2003: PhD in Mathematics,  Lomonosov Moscow State University, Moscow.
  • 2004-2006: Marie Curie Fellow at CRM, Barcelona.
  • 2006-2008: Post-doctoral Fellow at the Scuola Normale Superiore, Pisa.
  • 2008-September 2012: ICREA Researcher at CRM, Barcelona.
  • 2009: ISAAC Award.
  • 2012: ICREA Research Professor at CRM, Barcelona.
  • 2013: Humboldt Research Fellowship for Experienced Researchers.

Research interests

My main research areas are 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

– Dyachenko M, Mukanov A & Tikhonov S 2019, ‘Uniform convergence of trigonometric series with general monotone coefficients’, Canadian Journal of Mathimatics, vol. 71, no. 6, pp 1445-1463.

– Gorbachev  D &  Tikhonov S 2019 ‘Doubling condition at the origin for non-negative positive definite  functions‘, Proc. AMS, vol. 147, no. 2, pp 609-618.

– Gorbachev DV, Ivanov VI & Tikhonov S 2019, ‘Positive L-p-Bounded Dunkl-Type Generalized Translation Operator and Its Applications’, Constructive Approximation, 49, 3, 555 – 605.

– Abell M, Iacob E, Stokolos A, Taylor S, Tikhonov S & Zhu J (Eds.) 2019, Topics in Classical and Modern Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Basel.

– Dai F,  Prymak A, Temlyakov V & Tikhonov S 2019, ‘Integral norm discretization and related problems’, Russian Math. Surveys, vol. 74, pp 579-630.

– Dyachenko M, Mukanov A & Tikhonov S 2019, ‘Smoothness of functions and Fourier coefficients’, Sbornik: Mathematics, 210, 7, 994 – 1018.

Selected research activities

Conference and seminar talks:

  • Beijing (2), Budapest, Moscow (2)

Advanced courses:

  • CRM, Barcelona and Shanghai Jiao Tong University, China

Managerial Activities:

  • Main co-organizer of the research program “Approximation, sampling and compression in data science”, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January-June, 2019
  • Main co-organizer of the workshop “Approximation, sampling, and compression in high dimensional problems”, Isaac Newton Institute for Mathematical Sciences, Cambridge

Member of Editorial board:

  • Journal of Fourier Analysis and Applications
  • Demonstratio Mathematica
  • Jaen Journal on Approximation
  • Analysis Mathematica
  • Journal of Mathematical Analysis and Applications
  • Bulletin of Mathematical Analysis and Applications

Honors and Awards:

  • Visiting Fellow, Pembroke College, Cambridge University, UK
  • Simons Fellow, The Isaac Newton Institute for Mathematical Sciences, UK