Related papers: Polyfold and SFT Notes I: A Primer on Polyfolds an…
The increasing interest in the phenomenology of the Standard Model Effective Field Theory (SMEFT), has led to the development of a wide spectrum of public codes which implement automatically different aspects of the SMEFT for…
This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.
The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate…
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments.
This is a survey of some recent results concerning polynomial inequalities and polynomial approximation of functions in the complex plane. The results are achieved by the application of methods and techniques of modern geometric function…
This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open…
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
This article details a construction of symplectic foliations on 3-dimensional orientable riemannian manifolds from harmonic forms; and how it suggests a topological approach to Poisson's equation and newtonian gravity.
This is an expository and introductory note on some results obtained in "Coisotropic embeddings in Poisson manifolds" (ArXiv math/0611480). Some original material is contained in the last two sections, where we consider linear Poisson…
This book deals with the elementary theory of cyclotomic fields, cyclotomic function fields, abelian extensions, genus fields, $p$--extensions, Drinfeld modules and class field theory. The text is in Spanish.
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with…
Contents: I. Introduction II. Manifolds in random media III. Thermal fluctuations without disorder IV. Random forces V. Random potential: variational approach VI. Physical interpretation of the solution
This volume contains the papers presented at the 1st workshop on Quantitative Formal Methods: Theory and Applications, which was held in Eindhoven on 3 November 2009 as part of the International Symposium on Formal Methods 2009. This volume…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This thesis is divided into four chapters. The first chapter discusses the relationship between stacks on a site and groupoids internal to the site. It includes a rigorous proof of the folklore result that there is an equivalence between…
In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in…