The C.I.M.E. Summer School at Como in 1986 was the first in that series on the subject of combinatorial optimization. Situated between combinatorics, computer science and operations research, the subject draws on a variety of mathematical methods to deal with problems motivated by real-life applications. Recent research has focussed on the connections to theoretical computer science, in particular to computational complexity and algorithmic issues. The Summer School's activity centered on the 4 main lecture courses, the notes of which are included in this volume:
The C.I.M.E. Summer School at Como in 1986 was the first in that series on the subject of combinatorial optimization. Situated between combinatorics, ...
Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. This text illustrates developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) is included.
Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. This text illustrates developments of this theory...
In recent years the subject of relativistic fluid dynamics has found substantial applications in astrophysics and cosmology (theories of gravitational collapse, models of neutron stars, galaxy formation), as well as in plasma physics (relativistic fluids have been considered as models for relativistic particle beams) and nuclear physics (relativistic fluids are currently used in the analysis of the heavy ion reactions). Modern methods of analysis and differential geometry have now also been introduced. The International C.I.M.E. Course brought together expertise and interest from several...
In recent years the subject of relativistic fluid dynamics has found substantial applications in astrophysics and cosmology (theories of gravitational...
This volume contains the notes of the lectures delivered at the CIME course GeometricAnalysis andPDEsduringtheweekofJune11 162007inCetraro (Cosenza). The school consisted in six courses held by M. Gursky (PDEs in Conformal Geometry), E. Lanconelli (Heat kernels in sub-Riemannian s- tings), A. Malchiodi(Concentration of solutions for some singularly perturbed Neumann problems), G. Tarantello (On some elliptic problems in the study of selfdual Chern-Simons vortices), X. J. Wang (Thek-Hessian Equation)and P. Yang (Minimal Surfaces in CR Geometry). Geometric PDEs are a ?eld of research which is...
This volume contains the notes of the lectures delivered at the CIME course GeometricAnalysis andPDEsduringtheweekofJune11 162007inCetraro (Cosenza). ...
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other.
This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in...
Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, th...
This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro, Italy, from July 1 to 7, 2007. The Nonlinear Optimization problem of main concern here is the problem n of determining a vector of decision variables x ? R that minimizes (ma- n mizes) an objective function f(-): R ? R, when x is restricted to belong n to some feasible setF? R, usually described by a set of equality and - n n m equality constraints: F = {x ? R: h(x)=0, h(-): R ? R; g(x) ? 0, n p g(-): R ? R }; of course it is intended that at...
This volume collects the expanded notes of four series of lectures given on the occasion of the CIME course on Nonlinear Optimization held in Cetraro,...
Presenting a review of advanced technological problems in the glass industry and of the mathematics involved, this volume describes problems which are typical in glass manufacturing as well as covering a wide spectrum of complementary subjects.
Presenting a review of advanced technological problems in the glass industry and of the mathematics involved, this volume describes problems which are...
This volume collects the notes of the CIME course "Nonlinear PDE's and applications" held in Cetraro (Italy) on June 23-28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cedric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics...
This volume collects the notes of the CIME course "Nonlinear PDE's and applications" held in Cetraro (Italy) on June 23-28, 2008. It consists of four ...
This text is based on the lectures given at the CIME Summer Centre 'Quantum Many Body Systems' held in the summer of 2010. It provides a tutorial introduction to advances in the mathematics of interacting systems, written by four leading experts in the field.
This text is based on the lectures given at the CIME Summer Centre 'Quantum Many Body Systems' held in the summer of 2010. It provides a tutorial intr...