Research Interests

Dr. Binev is a well-known specialist in nonlinear and adaptive approximation and recognized for establishing theoretical results for optimal convergence rates in adaptive finite element methods. He has been participating in various interdisciplinary research groups and has established several international collaborations for applying advanced mathematical methods in electron microscopy. He is a key participant in the research group that developed a record-holding procedure to consistently obtain a picometer precision measurements in scanning transmission electron microscopy. Dr. Binev is also working in mathematical learning theory, data assimilation, reduced modeling, and uncertainty quantification. He has presented more than a hundred invited talks on various international conferences and workshops. His research has been funded by several agencies and foundations over the years, with total grants amount exceeding $10M.

Education

• Ph.D. in Computational Mathematics, University of Sofia, Bulgaria (1985)
• M.S. in Mathematical Modeling, University of Sofia, Bulgaria (1980)

Experience

Tenure/Tenure-Track Positions

• Professor, University of South Carolina (2017 - present)
• Associate Professor, University of South Carolina (2007 – 2016)
• Associate Professor, University of Sofia, Bulgaria (1993 – 2006)
• Assistant Professor, University of Sofia, Bulgaria (1984 – 1993)

Visiting and Research Positions

• Visiting Professor, RWTH-Aachen University (Spring 2014)
• Visiting Professor, Texas A&M University (Fall 2013)
• Research Professor, University of South Carolina (2000 – 2007)
• Visiting Professor, University of South Florida (Spring 1999)
• Visiting Professor, University of Greenwich, UK (Fall 1997)
• Visiting Professor, University of Duisburg, Germany (Fall 1995)
• DAAD Research Fellow, University of Duisburg, Germany (1991-1992)
• Visiting Professor, University of South Florida (Fall 1990)
• Postdoctoral Research Fellow, Steklov Mathematical Institute, Russia (Fall 1986)

Courses Taught

At USC

• MATH 122: Calculus for Business Administration and Social Sciences
• MATH 141: Calculus I
• MATH 142: Calculus II
• MATH 174: Discrete Mathematics for Computer Science
• MATH 241: Vector Calculus
• MATH 242: Elemetary Differential Equations
• MATH 344: Applied Linear Algebra
• MATH 522: Wavelets
• MATH 526: Numerical Linear Algebra
• MATH 527: Numerical Analysis
• MATH 544: Linear Algebra
• MATH 550: Vector Analysis
• MATH 574: Discrete Mathematics
• MATH 706: Numerical Linear Algebra
• MATH 708: Foundations of Computational Mathematics I
• MATH 709: Foundations of Computational Mathematics II
• MATH 720: Applied Mathematics I
• MATH 721: Applied Mathematics II
• MATH 726: Differential Equations I
• MATH 727: Differential Equations II
• SCHC 411: Mathematics of Data

At other universities

• College Algebra
• Applied Finite Mathematics
• Engineering Calculus
• Calculus
• Numerical Analysis
• Numerical Methods for PDE's
• Computer Graphics
• Algorithms
• Wavelets
• Splines and Their Applications
• Multivariate Splines
• Curves and Surfaces in CAGD
• Wavelets and Their Applications
• Geometric Modeling
• Advanced Computer Graphics
• Image Processing

Selected Publications

• P. Binev, W. Dahmen, R. DeVore, Adaptive Finite Element Methods with Convergence Rates, Numerische Mathematik 97 (2004), 219-268.
• P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, and P. Wojtaszczyk, Convergence Rates for Greedy Algorithms in Reduced Basis Methods, SIAM J. Math. Anal. 43 (2011),1457–1472.
• A.B. Yankovich, B. Berkels, W. Dahmen, P. Binev, S.I. Sanchez, S.A. Bradley, Ao Li, I. Szlufarska, and P.M. Voyles, Picometre-precision analysis of scanning transmission electron microscopy images of platinum nanocatalysts, Nature Communications 5 (2014), Article number: 4155.
• P. Binev, R. DeVore, Fast Computation in Adaptive Tree Approximation, Numerische Mathematik 97 (2004), 193-217.
• P. Binev, Tree approximation for hp-adaptivity, SIAM Journal on Numerical Analysis 56 (2018), 3346-3357.
• P. Binev, A. Cohen, W. Dahmen, R. DeVore, and V Temlyakov, Universal algorithms for learning theory - part i: piecewise constant functions, Journal of Machine Learning Research 6 (2005), 1297-1321.
• P. Binev, W. Dahmen, R. DeVore, P. Lamby, D. Savu, and R. Sharpley, Compressed Sensing and Electron Microscopy, in Modeling Nanoscale Imaging in Electron Microscopy, T. Vogt, W. Dahmen, and P. Binev (Eds.), Springer, 2012, p. 73-126.
• P. Binev, W. Dahmen, and P. Lamby, Fast high-dimensional approximation with sparse occupancy trees, J. Computational and Applied Mathematics 235 (2011), 2063–2076.
• P. Binev, A. Cohen, W. Dahmen, and R. DeVore, Classification Algorithms using Adaptive Partitioning, Annals of Statistics 42 (2014), 2141-2163.