Divided into two parts, this book targets graduate students and researchers who want to learn about variable Lebesgue spaces and partial differential equations. Part I provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces likethe classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally in the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. Part IIof...
Divided into two parts, this book targets graduate students and researchers who want to learn about variable Lebesgue spaces and partial differential ...
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a...
This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal wi...
In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometry. This book originated from two courses delivered by the authors at the CRM and provides a self-contained introduction to these topics, covering most of the recent advances. The first part, by Semyon Alesker, provides an introduction to the theory of convex valuations with emphasis on recent developments. In particular, it presents the new structures on the space of valuations discovered after Alesker's irreducibility theorem. The newly...
In the last years there has been significant progress in the theory of valuations, which in turn has led to important achievements in integral geometr...
This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification...
This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete ex...
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.
Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps.
Both advanced graduate students and...
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces m...
This book collects the notes of the lectures given in the "Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanics (DANCE Winter School)" held at Centre de Recerca Matematica (CRM) from January 27th to 31th, 2014. The notes consist of three series of lectures. One is dedicated to the study of periodic solutions of autonomous differential systems in R DEGREESn via the averaging theory, and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying central configurations. And the last one, given by Carles Simo,...
This book collects the notes of the lectures given in the "Advanced Course on Central Configurations, Periodic Orbits and Beyond in Celestial Mechanic...
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012).
The notes of the course by Vlad Bally, co-authored with Lucia Caramellino, develop integration by parts formulas in an abstract setting, extending Malliavin's work on abstract Wiener spaces. The results are applied to prove absolute continuity and regularity results for the density for a broad class of random processes.
Rama Cont's notes provide an introduction to the Funcional Ito Calculus, a non-anticipative functional calculus that...
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2...
This volume is based on four advanced courses held at the Centre de Recerca Matematica (CRM), Barcelona. It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces. The lectures focus on the geometry of moduli spaces which are mostly associated to compact Riemann surfaces, and are presented from both classical and quantum perspectives.
"
This volume is based on four advanced courses held at the Centre de Recerca Matematica (CRM), Barcelona. It presents both background information an...
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matematica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields.
Native to actual problem-solving challenges in mechanics, the...
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matematica in Barcelona, these lecture notes address t...
This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis.
Rene Schilling s notes are an expanded version of his course on Levy and Levy-type processes, the purpose of which is two-fold: on the one hand, the course presents in detail selected properties of the Levy processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Levy-Ito decomposition. On the other, it identifies the infinitesimal generator of the Levy...
This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Rene Schilling, respectively, at the second Barcelona Summe...
