The Viggo Brun Prize for 2026 is awarded to:

Aleksei Kulikov

for his original and influential contributions to harmonic analysis, complex analysis, and time-frequency analysis, especially for his work on uncertainty principles, Fourier interpolation, sharp inequalities for spaces of analytic functions, and Gabor frames.

Aleksei Kulikov received his PhD from the Norwegian University of Science and Technology in 2022, under the supervision of Kristian Seip. In only a few years, he has produced a remarkable body of work spanning several areas of analysis. His research is united by a broad modern view of uncertainty principles: the study of how functions, signals, analytic objects, or quantum states may be localized, represented, or reconstructed.

One of Kulikov’s most striking early achievements is the paper “Functionals with extrema at reproducing kernels”, published in Geometric and Functional Analysis (2022). In this short and beautiful work, he proved sharp inequalities for natural functionals on Hardy and Bergman spaces, showing that the extremal functions are precisely the normalized reproducing kernels. The paper solved contractivity conjectures of Pavlović and of Brevig, Ortega-Cerdà, Seip and Zhao, as well as a Wehrl-type entropy conjecture of Lieb and Solovej for the group SU(1,1). The proof is characteristic of Kulikov’s style: a difficult functional-analytic problem is transformed into a geometric one and then solved by applying the hyperbolic isoperimetric inequality.

This work also yields a unified approach to results about Wehrl entropy in different geometric settings. In particular, Kulikov’s approach gives a clean new proof of the main results of an Acta Mathematica paper of Lieb and Solovej from 2014. This more general point of view was elaborated in “A monotonicity theorem for subharmonic functions on manifolds”, with Fabio Nicola, Joaquim Ortega-Cerdà and Paolo Tilli, in Advances in Mathematics (2025). There Kulikov and his coauthors developed a unified approach to sharp contractivity and entropy inequalities in several classical geometric settings; in particular, their theorem gives a complete solution of the SU(2) version of the Wehrl entropy conjecture, with coherent states as the only extremizers.

A second major direction in Kulikov’s work concerns Fourier interpolation and uniqueness. In “Fourier interpolation and time-frequency localization”, in Journal of Fourier Analysis and Applications (2021), he proved a general density theorem for interpolation formulas expressing a function through values of the function and its Fourier transform on two discrete sets. The topic originates in the work of Danylo Radchenko and Maryna Viazovska,  and belongs to the circle of ideas around the Landau–Pollak–Slepian theory of time-frequency concentration. Kulikov resolved the density problem in a most satisfactory way, finding the right quantitative form of the necessary condition.

This line of research later led to impressive refinements of eigenvalue estimates for the classical time-frequency localization operator of Landau, Pollak, and Slepian. In “Exponential lower bound for the eigenvalues of the time-frequency localization operator before the plunge region”, in Applied and Computational Harmonic Analysis (2024), Kulikov proves that the relevant eigenvalues remain exponentially close to one throughout the full pre-plunge regime, improving a result of Bonami, Jaming and Karoui. In the later preprint “Sharp estimates for eigenvalues of localization operators before the plunge region” (2026), he gives matching sharp estimates both for the classical time-frequency localization operator and for the coherent state transform, revealing subtle differences between the two settings. 

Kulikov’s work on Fourier interpolation also led to the important joint work “Fourier uniqueness and non-uniqueness pairs”, with Fedor Nazarov and Mikhail Sodin, published in Journal of Mathematical Physics, Analysis, Geometry (2025). The paper gives general analytic conditions for the existence of Fourier interpolation formulas, expressing a function through its values and the values of its Fourier transform along two respective discrete sets. This fundamental work largely clarifies what can be achieved by classical analysis in this problem. It is a tour de force, combining real and complex analysis, Fourier analysis, and delicate estimates.

Another outstanding body of work concerns Gabor frames, done in collaboration with Yurii Belov and Yurii Lyubarskii. Together they developed a remarkable series of results on Gabor systems generated by rational functions and Cauchy kernels. This line of work culminated in the Inventiones Mathematicae paper “Gabor frames for rational functions” (2023), where they essentially clarified the conditions for when the Gabor system associated with a rational window function is a frame. The takeaway from this work is that Daubechies’s conjecture for Gabor systems is “almost always” true, but there is a subtle set of exceptions, mostly of arithmetic nature.

The same circle of ideas includes “Irregular Gabor frames of Cauchy kernels”, Applied and Computational Harmonic Analysis (2022), and “Gabor frame operator for the Cauchy kernel”, with Belov and Lyubarskii, as well as more recent work with Belov on compactly supported functions and functions supported on a semi-axis. Taken together, these papers form a far-reaching development of classical Gabor analysis. As a result, the problems that emerged in the work of Daubechies and others around 1990 about “generic” window functions now seem much more tangible.

In conclusion, Aleksei Kulikov has, in a remarkably short time, established himself as one of the leading young researchers in analysis. His work is deep, elegant, and original, and it has already had a substantial impact on the study of uncertainty principles and on several related areas of modern analysis.