Foundations of Computational Mathematics

Felipe Cucker is Chair Professor of Mathematics at the City University of Hong Kong. His research covers a variety of subjects including semi-algebraic geometry, computer algebra, complexity, emergence in decentralized systems (in particular, emergence of languages and flocking), learning theory, and foundational aspects of numerical analysis. He serves on the editorial board of several journals and is Managing Editor of the journal Foundations of Computational Mathematics, published by the society of the same name.

Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract).- Essentially Smooth Lipschitz Functions: Compositions and Chain Rules.- Junction Detection and Filtering.- Recognition in Hierarchical Models.- Continuity ?-Algebras (Extended Abstract).- Condition Number Analysis for Sparse Polynomial Systems.- Residues in the Torus and Toric Varieties.- Piecewise Smooth Orthonormal Factors for Fundamental Solution Matrices.- Algorithms for computing finite semigroups.- Extended Grzegorczyk Hierarchy in the BSS Model of Computability.- Affine-Invariant Symmetry Sets.- On the Qualitative Properties of Modified Equations.- Numerical Methods on (and off) Manifolds.- On One Computational Scheme Solving the Nonstationary Schrödinger Equation with Polynomial Nonlinearity.- Newton Iteration Towards a Cluster of Polynomial Zeros.- Szemerédi's Regularity Lemma for Sparse Graphs.- Questions on Attractors of 3-Manifolds.- A Trust-Region SLCP Model Algorithm for Nonlinear Programming.- On the height used by additives BSS machines.- The Space Complexity of Elimination Theory: Upper Bounds.- Global Stochastic Recursive Algorithms.- Dynamical Recognizers: Real-time Language Recognition by Analog Computers (Extended Abstract).- Solving special polynomial systems by using structured matrices and algebraic residues.- Numerical Integration of Differential Equations on Homogeneous Manifolds.- A Convergence proof of an Iterative Subspace Method for Eigenvalues Problems.- Regularity of Minimizers of the Mumford-Shah Functional.- Tests and Constructions of Irreducible Polynomials over Finite Fields.- Numerical Linear Algebra in Optical Imaging.- Explicit symplectic integration of rod dynamics.- Toric Laminations, Sparse Generalized Characteristic Polynomials, and a Refinementof Hilbert's Tenth Problem.- Finite-Dimensional Feedback Control of a Scalar Reaction-Diffusion Equation via Inertial Manifold Theory.- Computational aspects of jacobian matrices.- Rigid body dynamics and measure differential inclusions.- Linear decision lists and partitioning algorithms for the construction of neural networks.- Ill-Posedness and Finite Precision Arithmetic: A Complexity Analysis for Interior Point Methods.- Iterated Commutators, Lie's Reduction Method and Ordinary Differential Equations on Matrix Lie Groups.