## Prize Description

The Vasil A. Popov Prize was established in memory of the late Professor Vasil A. Popov of Bulgaria in recognition of his outstanding contributions to mathematics. The Prize was created in 1995 and has been maintained solely by contributions from his colleagues, friends, and those who support the existence of such a prize. The Prize recognizes distinguished research accomplishments in Approximation Theory and related areas of mathematics. Eligibility for the Prize is restricted to young mathematicians removed less than 6 years from their doctoral degree.

The Vasil A. Popov Prize, which consists of an engraved marble trophy and a cash award of 2000 euros, is awarded every third year at the Foundation of Computational Mathematics (FoCM) conference.

The Vasil A. Popov Prize is good for mathematics ! It brings recognition to an important area of mathematical research, bridging theory and applications, and encourages young talented mathematicians engaging into this area.

The First Prize in 1995 was awarded to **Albert Cohen** (Paris VI) ; the Second Prize in 1998 to **Arno Kuijlaars** (Katholieke Universiteit in Leuven, Belgium) ; the Third Prize in 2001 to **Emmanuel Candes** (Cal Tech) ; the Fourth Prize in 2004 to **Serguei Denissov** (University of Wisconsin-Madison) ; the Fifth Prize in 2007 to **Mauro Maggioni** (Duke University) ; the Sixth Prize in 2010 to **Joel A. Tropp** (California Institute of Technology) ; the Seventh Prize in 2013 to **Andriy Bondarenko** (National Taras Shevchenko University of Kyiv) ; the Eighth Prize in 2016 to **Jean-Marie Mirebeau** (CNRS, Université Paris-Sud) ; the Ninth Prize in 2020 to **Danylo Radchenko** (ETH, Zurich) ; and the Tenth Prize in 2023 to **Matthew Colbrook** (Cambridge University).

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## Vasil A. Popov

Vasil Popov was born in Sofia, Bulgaria, on January 14, 1942. His father was a Doctor in Philosophy and his mother, a leading French translator, was a Chevalier of the Order of Arts and Literature. From the early days of communism his father was prosecuted for his political ideas. This left lasting marks on Vasil’s youth and affected his career choices later in life. He was married to Alexandra and had two sons : Alexandar and Atanas.

Young Vasil grew up smart and outgoing with a broad range of interests and skills. He played the piano, and took the full university courses on physics and mathematics simultaneously in only three and half years. His father’s background made science one of the few apolitical career options available. In 1965 Vasil Popov graduated from the Department of Mathematics at Sofia University and took a permanent position at the Institute of Mathematics of the Bulgarian Academy of Sciences. He became a Senior scientist in 1974, a Full Professor in 1981, and the youngest Corresponding Member of the Bulgarian Academy of Sciences in 1984. Throughout his career he taught mathematics at the Sofia University. He also visited many international research centers, such as the Steklov Institute in Moscow, the University of South Carolina in Columbia, and Temple University in Philadelphia. Vasil Popov died in Philadelphia on May 31, 1990.

His research focused primarily in Approximation theory. His PhD thesis « Convex Approximation’’ was written under the supervision of Blagovest Sendov and defended in 1971. He received a Doctor of Sciences degree in 1977 with a dissertation on « Direct and Converse Theorems in Approximation Theory ». Dr. Popov’s work included numerous publications and textbooks. He helped establish Bulgaria as an international scientific center by organizing multiple conferences and seminars. He guided more than 15 doctoral students, many of them continuing his work in Approximation theory and related areas in mathematics today.

Vasil Popov’s talent and creative energy made him a burning star that set early. His death was a great loss for the Bulgarian mathematics community, but his achievements and ideas continue to inspire many followers.

## Previous Winners

The Vasil A. Popov Prize was initiated in 1995 to honor the life and mathematics of Vasil Popov (1942-1990), the Bulgarian analyst best known for his work in Nonlinear Approximation. This Prize is awarded every 3 years by a select committee of eminent mathematicians, and is given for outstanding research done in approximation theory and other fields related to Vasil Popov’s work. Only young mathematicians— ie, a person who has received their PhD degree within the past six years— are eligible for the prize. Following is a list of previous winners of this prize since its inception.

The Tenth Vasil A. Popov Prize was awarded on June 19, 2023 to Matthew Colbrook from the University of Cambridge at the 2023 Foundations of Computational Mathematics (FoCM) conference.

Matthew (Matt) was recognized for his outstanding contributions to approximation theory, particularly his work on the approximation of spectral properties of operators in infinite-dimensional spaces and the approximation power and trainability of neural networks. Computing approximations of spectra in infinite dimensions has been a significant challenge for mathematicians since the 1950s. Matt has introduced new algorithms that converge and come with explicit approximation guarantees. He has also developed a myriad of techniques yielding optimal approximation results for different spectral properties of operators, classifying when this can and cannot be done in the Solvability Complexity Index Hierarchy, and solving other open problems such as approximating generic spectral measures, geometric spectra, and (data-driven) Koopman operators in dynamical systems. Parallel to this work, Matt has contributed significantly to the problem of approximation power and trainability of neural networks. For example, in a paper published in Proceedings of the National Academy of Sciences (PNAS), Matt and his collaborators have shown that there are problems where stable and accurate neural networks exist, yet no training algorithm can produce such a network.

The Prize, consisting of a pyramid trophy and a cash award of $2000, was presented to Matt by Albert Cohen, Chair of the Popov Prize Selection Committee. After the prize ceremony, Matt gave a lecture at the conference.

Matt is an Assistant Professor at the University of Cambridge. He received his PhD in September 2020 from the University of Cambridge under the supervision of Anders C. Hansen.

The Ninth Vasil A. Popov Prize was awarded on June 5, 2020 to **Danylo V. Radchenko** from* ETH, Zürich*.

Danylo V. Radchenko was recognized for his outstanding contributions to Approximation Theory, in particular, to the theory of spherical designs. Together with Andriy V. Bondarenko and Maryna S. Viazovska he settled a long-standing conjecture by Korevaar and Meyers on optimal asymptotic bounds for spherical t-designs. Later, in a joint paper with H. Cohn, A. Kumar, S. D. Miller and M. S. Viazoska they proved the optimality of the Leech lattice among all 24-dimensional sphere packings. Danylo Radchenko has also contributed to the Theory of Shape Preserving Approximation and to Non-uniform Sampling Theory in relation with Fourier Analysis. Parallel to Approximation Theory, he has been working in Number Theory, in particular, on Dedekind zeta functions and on cross-ratios related to the work of Goncharov.

The Prize, which consists of a marble pyramid trophy and a cash award of 2000 euros, will be presented to Radchenko by Albert Cohen of Sorbonne Université, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee were Wolfgang Dahmen, Karlheinz Grochenig, Pencho Petrushev, Peter Oswald, and Vilmos Totik. The Popov Prize awarding ceremony initially scheduled at the FoCM 2020 Conference in Vancouver has been postponed due to COVID-19.

Danylo V. Radchenko holds a Hermann-Weyl-Instructor position at the Institute for Mathematical Research of ETH Zurich. He received his PhD in July 2016 from University of Bonn, under the supervision of Don Zagier.

The Eighth Vasil A. Popov Prize was awarded on May 23, 2016 to **Jean-Marie Mirebeau**, from *CNRS and Université Paris Saclay* at the 15th International Conference on Approximation Theory held in San Antonio, Texas.

Jean-Marie Mirebeau was recognized for his outstanding contributions to the development and analysis of nonlinear and adaptive approximation methods that account for local anisotropic features. In particular, he has identified the algebraic structures that lead to the characterization of the optimal aspect ratio of simplices in finite element approximation, revealing among others the role played by the beautiful Hilbert invariant polynomial theory. His work also shed light on the properties of Riemann metrics that should be prescribed in mesh generation algorithms for optimizing the compromise between complexity and accuracy measured in various relevant norms. Motivated by image processing applications, Mirebeau developed powerful discretization techniques that allow to properly treat anisotropy in partial differential equations when a regular square grid is imposed. A critical role in these developments is played by Laguerre Voronoi diagrams and reduced lattice bases.

The Prize, which consists of a marble pyramid trophy and a cash award of $2000, was presented to Mirebeau by Pencho Petrushev of the University of South Carolina, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee were Wolfgang Dahmen, Arno Kuijlaars, Paul Nevai, Peter Oswald, and Edward Saff. After the Prize awarding ceremony, Mirebeau gave a lecture at the Conference entitled « Adaptive and Anisotropic Approximation Tools and Techniques ».

Jean-Marie Mirebeau holds a research position at the CNRS, Université Paris-Saclay, France. He received his PhD in December 2010, from the Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, under the supervision of Albert Cohen.

The Seventh Vasil A. Popov Prize was awarded on April 8, 2013 to **Andriy Bondarenko**, *National Taras Shevchenko University of Kyiv, Ukraine*, during the Fourteenth International Conference on Approximation Theory held in San Antonio, Texas.

Andriy Bondarenko was recognized for his outstanding contributions to Approximation Theory. He along with Radchenko and Viazovska solved the spherical t-design conjecture by Korevaar and Meyers concerning optimal approximation of integrals over the sphere by arithmetic means of values of the integrand. This result beautifully illustrates the power of the fixed-point method to approximation problems. Andriy Bondarenko has also advanced powerful new ideas in other areas of Approximation Theory, in particular, in monotone rational approximation, one of Vasil A. Popov’s favorite research areas.

The Prize, which consists of a marble pyramid trophy and a cash award of $2000, was presented to Andriy Bondarenko by Pencho Petrushev of the University of South Carolina, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee were Albert Cohen, Arno Kuijlaars, Wolfgang Dahmen, Paul Nevai, Allan Pinkus, and Edward Saff. After the Prize awarding ceremony, Andriy Bondarenko gave a plenary lecture at the Conference entitled « Fixed Point Theorems in Approximation Theory ».

Andriy Bondarenko is an Assistant Professor at the Kyiv National Taras Shevchenko University, Ukraine. He received his PhD from the same university in June 2007 under the supervision of Igor Schevchuk and Jacek Gilewicz.

The Sixth Vasil Popov Prize was awarded on March 8, 2010 to **Joel A. Tropp**, * California Institute of Technology*, during the Thirteenth International Conference on Approximation Theory held in San Antonio, Texas.

Joel Tropp was recognized for his outstanding contributions to the development of sparse reconstruction methods in the context of approximation from redundant systems, greedy algorithms, and most recently compressed sensing. In particular, he has shown that greedy algorithms will with high probability exactly recover sparse vectors from random measurements e.g. based on Gaussian or Bernoulli distributions. This was a cornerstone result in showing the efficacy of greedy algorithms for decoding in compressed sensing. Another impressive result by Joel Tropp is the now famous COSAMP algorithm of Needell and Tropp, which were the first to establish the optimal performance of greedy decoding in ℓ^{2}. Tropp’s work has significantly advanced the understanding of greedy algorithms and sublinear reconstruction algorithms in new highly relevant application contexts.

The Prize which consists of a marble pyramid trophy and a cash award of $2000 was presented to Joel Tropp by Pencho Petrushev of the University of South Carolina, Chair of the Popov Prize Selection Committee. The other members of the Selection Committee are Albert Cohen, Arno Kuijlaars, Wolfgang Dahmen, Paul Nevai, Allan Pinkus, and Edward Saff. After the Prize awarding, Joel Tropp gave a plenary lecture at the Conference entitled « Sparse Solutions to Linear Inverse Problems ».

The Fifth Vasil Popov Prize was awarded on March 6, 2007 to **Mauro Maggioni**, * Duke University*, during the Twelfth International Conference on Approximation Theory held in San Antonio, Texas.

Mauro Maggioni was recognized for his contributions to Harmonic analysis on graphs, in particular for his work on diffusion geometry and the construction of Multiscale analysis and wavelets based on diffusion processes on graphs. Maggioni has introduced novel ideas and powerful new techniques which allow him to seamlessly integrate empirical applied mathematics with the deepest theoretical tools in pure mathematics. His work has already had a seminal impact in the fields of information organization, machine learning, spectral graph theory, image analysis, and medical diagnostics.

The Prize, which consists of a marble pyramid trophy and a cash award, was presented to Maggioni by Pencho Petrushev of the University of South Carolina on behalf of the Selection Committee. The other members of the Committee were Charles Chui, Wolfgang Dahmen, Paul Nevai, Allan Pinkus, and Edward Saff. After the Prize presentation, Mauro Maggioni presented a plenary lecture entitled « Diffusion processes on graphs and multiscale analysis of highdimensional data. »

The Fourth Vasil Popov Prize was awarded on May 19, 2004 to **Serguei Denissov**, * California Institute of Technology*, during the Eleventh International Conference on Approximation Theory held in Gatlinburg, Tennessee.

Serguei Denissov was recognized for his contributions to Spectral theory and Orthogonal polynomials. He proved the continuous analog of Rakhmanov’s Theorem for Jacobi matrices, which settled a conjecture of Paul Nevai that had been open for more than 15 years. Denissov has introduced new ideas and powerful new techniques in Spectral theory that enabled him to solve deep problems. In particular, he was the first to show that there exist Schrödinger operators with square integrable potentials for which absolutely continuous and singular spectrum co-exist on the same spectral interval.

The Prize which consists of a marble pyramid trophy and a cash award, was presented to Denissov by Pencho Petrushev of the University of South Carolina on behalf of the selection committee. The other members of the committee were Ronald DeVore, Charles Chui, Paul Nevai, Allan Pinkus, and Edward Saff. After the Prize presentation, Denissov presented a plenary lecture entitled « On Different Applications of Approximation Theory in Mathematical Physics. »

The Third Vasil Popov Prize was awarded on March 28, 2001 to **Emmanuel Candes**, * California Institute of Technology*, during the Tenth International Conference on Approximation Theory held in St. Louis, Missouri.

Emmanuel Candes was recognized for the development of ridgelets, curvelets, and other descendants of wavelets. These novel building blocks provide more efficient representations of functions that have singularities along curves. Research in this area is motivated by potential applications to image and data processing. In addition to the development of ridgelet frames, Candes has solved deep problems in nonlinear approximation by linear combinations of ridgelets. Candes received a PhD in statistics from the Stanford University, in 1998, under the supervision of David Donoho.

The Second Vasil Popov Prize was awarded in January 1998 to **Arno Kuijlaars**, * atholieke Universiteit in Leuven, Belgium*, during the Ninth International Conference on Approximation Theory held in Nashville, Tennessee.

Kuijlaars was cited for his innovative work on Chebyshev quadrature problems for the sphere in arbitrary dimensions, his solutions of several difficult problems posed by V. Totik concerning approximation by polynomials with varying weights, and for his contributions to the asymptotic theory for minimum energy-point arrangements on the sphere. He completed his undergraduate studies in mathematics at the Technical University in Eindhoven, Netherlands, and his graduate work in 1991 at the University of Utrecht, under the direction of Emile Bertin.

Following graduate school, Kuijlaars completed postdoctoral work at the University of Amsterdam, where he worked closely with Korevaar. He then spent a year in the U.S., working with Ed Saff (University of South Florida), who presented the prize on behalf of the selection committee, and Walter Gautschi (Purdue University). He also completed a fellowship year working with Walter Van Assche at KU.

The First Vasil Popov Prize was awarded on January 9, 1995 to **Albert Cohen**, * Université de Paris, Dauphine, and ENSTA (École Nationale Supérieure des Techniques Avancées), *during the Eighth International Conference on Approximation Theory held in College Station, Texas.

Cohen’s recent work has « emphasized the connections between wavelet theory and approximation, especially in the context of nonlinear approximation, » says Ronald DeVore of the University of South Carolina, who chairs the prize committee. Cohen’s plenary lecture at the Texas conference was entitled « Nonlinear Wavelet Approximation in Image Compression.

Cohen received a PhD in 1990 from the Université de Paris, Dauphine, under the direction of Yves Meyer. His early research, done jointly with Ingrid Daubechies, was on the relation between wavelet theory and filter banks used in signal processing. This research « led to the design of certain filter banks (related to biorthogonal wavelets) that are widely used by engineers in image and signal processing and provided a deeper understanding of multiresolution analysis and refinement equations, » says DeVore. Cohen has also made significant contributions to the development of multiscale methods for Euclidean domains and to the construction of related numerical algorithms, DeVore adds.

## Selection Committee

The Selection Committee for the Vasil A. Popov Prize consists of :

Albert Cohen, Chair(Université Pierre et Marie Curie),Wolfgang Dahmen(RWTH Aachen and University of South Carolina),Karlheinz Gröchenig(Universität Wien),Carla Manni(Universita di Roma Tor Vergata),Pencho Petrushev, Co-Chair(University of South Carolina),Gabriele Steidl(Technische Universität Berlin), andVilmos Totik(University of Szeged).

## Donate now

Help us recognize and support the distinguished research accomplishments of young mathematicians working in Approximation Theory and related areas. The Popov prize fund is currently hosted by the ** Fondation Science Mathematiques de Paris (FSMP)**. All donations are directed to the Vasil A. Popov Prize ensuring that 100% of your contribution benefits the mathematicians we recognize with this award.

**Your support is very much appreciated !**