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Department of Mathematics

Directory

Peter Binev

Title: Professor
Department: Mathematics
College of Arts and Sciences
Email: binev@math.sc.edu
Phone: 803-576-6269
Office: Leconte 429C
Resources: My Website
Department of Mathematics
Peter Binev

Education

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

Experience

Tenure/Tenure-Track Positions:
2017 - Present Professor University of South Carolina
2007 - 2016 Associate Professor University of South Carolina
1993 - 2006 Associate Professor University of Sofia, Bulgaria
1984 - 1993 Assistant Professor University of Sofia, Bulgaria
 
Visiting and Research Positions:
Spring 2014 Visiting Professor RWTH-Aachen University
Fall 2013 Visiting Professor   Texas A&M University
2000-2007 Research Professor University of South Carolina
Spring 1999 Visiting Professor University of South Florida 
Fall 1997 Visiting Professor University of Greenwich, UK 
Fall 1995 Visiting Professor University of Duisburg, Germany
1991-1992 DAAD Research Fellow University of Duisburg, Germany
Fall 1990 Visiting Professor University of South Florida 
Fall 1986 Postdoctoral Research Fellow Steklov Mathematical Institute, Moscow
 

Courses Taught

At UofSC:
  • 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

Research

Dr. Binev is 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 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.

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.

 


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