Bücher der Reihe C.I.M.E. Foundation Subseries

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics.

This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues.The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes.This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.

The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.

The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro.

The summer school on Mathematics inspired by Biology was held at Martina Franca, Apulia, Italy in 1997. But the type of structure ranges from spatial (hadeler and maini in the deterministic setting, Durrett in the stochastic setting) to physiological (Diekmann) and order (Smith).

The book gives a survey of some recent developments in the theory of bundles on curves arising out of the work of Drinfeld and from insights coming from Theoretical Physics. Drinfeld Shtukas (Lectures by G. Drinfeld modules and Elliptic Sheaves (Lectures by U.

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini.

This volumebrings together four lecture courses on modern aspects of water waves. Thelectures provide a useful source for those who want to begin to investigate howmathematics can be used to improve our understanding of water wave phenomena.

Constantin presents the Euler equations of ideal incompressible fluids and the blow-up problem for the Navier-Stokes equations of viscous fluids, describing major mathematical questions of turbulence theory.

This book presents the state of the art in mathematical research on modelling the mechanics of biological systems - a science at the intersection between biology, mechanics and mathematics known as mechanobiology.

Pluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This CIME course focused on complex Monge-Ampere equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics.

Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

This book presents a series of challenging mathematical problems which arise in the modeling of Non-Newtonian fluid dynamics. It focuses in particular on the mathematical and physical modeling of a variety of contemporary problems, and provides some results. The flow properties of Non-Newtonian fluids differ in many ways from those of Newtonian fluids. Many biological fluids (blood, for instance) exhibit a non-Newtonian behavior, as do many naturally occurring or technologically relevant fluids such as molten polymers, oil, mud, lava, salt solutions, paint, and so on. The term "complex flows" usually refers to those fluids presenting an "internal structure" (fluid mixtures, solutions, multiphase flows, and so on). Modern research on complex flows has increased considerably in recent years due to the many biological and industrial applications.

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments.

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-24, 2006

Lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Bedlewo, PolandSeptember 4-9, 2006

In years, the subject of relativistic fluid dynamics has found substantial applications in astrophysics and cosmology, as well as in plasma physics and nuclear physics (relativistic fluids are used in the analysis of the heavy ion reactions). This title introduces modern methods of analysis and differential geometry.

Focusing on special matrices and matrices which are in some sense `near' to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra.

This volume presents a review of advanced technological problems in the glass industry and of the mathematics involved.

This volume contains the notes from five lecture courses devoted to nonautonomous differential systems, in which appropriate topological and dynamical techniques were described and applied to a variety of problems.

This book collects together a unique set of articles dedicated to several fundamental aspects of the Navier¿Stokes equations. As is well known, understanding the mathematical properties of these equations, along with their physical interpretation, constitutes one of the most challenging questions of applied mathematics. Indeed, the Navier-Stokes equations feature among the Clay Mathematics Institute's seven Millennium Prize Problems (existence of global in time, regular solutions corresponding to initial data of unrestricted magnitude). The text comprises three extensive contributions covering the following topics: (1) Operator-Valued H¿-calculus, R-boundedness, Fourier multipliers and maximal Lp-regularity theory for a large, abstract class of quasi-linear evolution problems with applications to Navier¿Stokes equations and other fluid model equations; (2) Classical existence, uniqueness and regularity theorems of solutions to the Navier¿Stokes initial-value problem, along with space-time partial regularity and investigation of the smoothness of the Lagrangean flow map; and (3) A complete mathematical theory of R-boundedness and maximal regularity with applications to free boundary problems for the Navier¿Stokes equations with and without surface tension.Offering a general mathematical framework that could be used to study fluid problems and, more generally, a wide class of abstract evolution equations, this volume is aimed at graduate students and researchers who want to become acquainted with fundamental problems related to the Navier¿Stokes equations.

This book offers a review of the vibrant areas of geometric representation theory and gauge theory, which are characterized by a merging of traditional techniques in representation theory with the use of powerful tools from algebraic geometry, and with strong inputs from physics.

Presenting a selection of topics in the area of nonlocal and nonlinear diffusions, this book places a particular emphasis on new emerging subjects such as nonlocal operators in stationary and evolutionary problems and their applications, swarming models and applications to biology and mathematical physics, and nonlocal variational problems.

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics.

Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability.