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Computer Science

D-Index
34
Citations
10035
World Ranking
11903
National Ranking
1478

Overview

Felipe Cucker is affiliated with the City University of Hong Kong in China. Their research spans multiple intersecting areas within computer science and mathematics, focusing particularly on computational theory and mathematics.

The main fields of study in Cucker's work include:

  • Computer Science
  • Mathematics

Within these fields, key subfields addressed are:

  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Algebra and Number Theory
  • Computational Mechanics
  • Mathematical Physics

Cucker's research covers a range of specialized topics such as:

  • Polynomial and algebraic computation
  • Topological and Geometric Data Analysis
  • Commutative Algebra and Its Applications
  • Advanced Numerical Analysis Techniques
  • Machine Learning and Algorithms
  • Homotopy and Cohomology in Algebraic Topology
  • Numerical Methods and Algorithms

Several recent papers authored or co-authored by Cucker illustrate the scope and progression of their scientific contributions:

  • Functional norms, condition numbers and numerical algorithms in algebraic geometry, 2022, Forum of Mathematics Sigma
  • On the Complexity of the Plantinga-Vegter Algorithm, 2022, Discrete & Computational Geometry
  • Computing the Homology of Semialgebraic Sets. II: General Formulas, 2021, Foundations of Computational Mathematics
  • Smale 17th Problem: Advances and Open Directions, 2021, New Zealand journal of mathematics
  • On the Complexity of the Plantinga-Vegter Algorithm, 2020, arXiv (Cornell University)

Cucker has frequently published in the following venues:

  • arXiv (Cornell University)
  • Foundations of Computational Mathematics
  • Forum of Mathematics Sigma
  • Discrete & Computational Geometry
  • New Zealand journal of mathematics

Cucker's collaborative network includes multiple frequent co-authors, specifically:

  • Josué Tonelli-Cueto
  • Alperen A. Ergür
  • Peter Bürgisser
  • Alexander Bastounis
  • Anders C. Hansen

Best Publications

  • On the mathematical foundations of learning

    Felipe Cucker;Steve Smale;Steve Smale

  • Complexity and Real Computation

    Lenore Blum;Felipe Cucker;Michael Shub;Steve Smale

  • Learning Theory: An Approximation Theory Viewpoint

    Felipe Cucker;Ding Xuan Zhou

  • On the mathematics of emergence

    Felipe Cucker;Steve Smale

  • Learning Theory

    Unknown

  • Best Choices for Regularization Parameters in Learning Theory: On the Bias-Variance Problem

    Felipe Cucker;Steve Smale

  • Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)

    Felipe Cucker;Ding Xuan Zhou

  • Condition : The Geometry of Numerical Algorithms

    Peter Brgisser;Felipe Cucker

  • A General Collision-Avoiding Flocking Framework

    F Cucker;Jiu-Gang Dong

  • Computational Complexity

    Unknown

  • Modeling Language Evolution

    Felipe Cucker;Steve Smale;Ding-Xuan Zhou

  • On a problem posed by Steve Smale

    Peter Bürgisser;Felipe Cucker

  • On mixed and componentwise condition numbers for Moore–Penrose inverse and linear least squares problems

    Felipe Cucker;Huaian Diao;Yimin Wei

  • A new condition number for linear programming

    Dennis Cheung;Felipe Cucker

  • Complexity estimates depending on condition and round-off error

    Felipe Cucker;Steve Smale

  • Flocking with informed agents

    Felipe Cucker;Cristián Huepe

  • ON THE CRITICAL EXPONENT FOR FLOCKS UNDER HIERARCHICAL LEADERSHIP

    Felipe Cucker;Jiu-Gang Dong

  • A Polynomial Time Algorithm for Diophantine Equations in One Variable

    F Cucker;P Koiran;S Smale

  • Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets

    Peter Bürgisser;Felipe Cucker

  • On digital nondeterminism

    Felipe Cucker;Martín Matamala

  • SIAM Journal on Optimization

    C Audet;H H Bauschke;L T Biegler;P L Combettes

  • Learning Theory: An Approximation Theory Viewpoint: Support vector machines for classification 157

    Felipe Cucker;Ding Xuan Zhou

  • Foundations of Computational Mathematics

    Felipe Cucker;Michael Shub

  • Learning Theory: An Approximation Theory Viewpoint: The framework of learning

    Felipe Cucker;Ding Xuan Zhou

  • Learning Theory: An Approximation Theory Viewpoint: Least squares regularization

    Felipe Cucker;Ding Xuan Zhou

Frequent Co-Authors

Michael J. Todd
Michael J. Todd Cornell University
Endre Süli
Endre Süli University of Oxford
Marek Karpinski
Marek Karpinski University of Bonn
Charles Audet
Charles Audet Polytechnique Montréal
Jorge Nocedal
Jorge Nocedal Northwestern University
Michael L. Overton
Michael L. Overton Courant Institute of Mathematical Sciences
Masao Fukushima
Masao Fukushima Kyoto University
Nicholas I. M. Gould
Nicholas I. M. Gould University of Oxford
Patrick L. Combettes
Patrick L. Combettes North Carolina State University
Lorenz T. Biegler
Lorenz T. Biegler Carnegie Mellon University

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