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# 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.

# Jean-Marie Mirebeau

The Eighth Vasil A. Popov Prize was awarded on May 23, 2016 to Jean-Marie Mirebeau, CNRS, Université Paris-Sud, France, during the Fifteenth 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-Sud, 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. ### 2013 - Seventh Prize Recipient # Andriy Bondarenko 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.

# Joel A. Tropp

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 ℓ2. 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".

# Mauro Maggioni

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."

# Serguei Denissov

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."

# Emmanuel Candes

The Third Vasil Popov Prize for 2001 was awarded on March 28, 2001, to Emmanuel Candes of the 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.

# Arno Kuijlaars

The Second Vasil Popov Prize was awarded in January 1998 to A.B.J. Kuijlaars, Katholieke 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.

# Albert Cohen

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.

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