Related papers: Lectures on meromorphic flat connections

This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews…

Initial-boundary value problems for 1-dimensional `completely integrable' equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it…

This paper presents a summary of the theoretical presentations to the international workshop "Diffraction 2006". The range of topics covered during the workshop was quite broad and this summary is therefore somewhat selective covering…

These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…

These are notes of lectures given at the Third School of Theoretical Physics in Jijel (Algeria, September 2009). The subject of these notes is differential geometry, complex and quaternionic structures with applications to theoretical…

We give sufficient conditions for three- or four-dimensional truncated Poincare-Dulac normal forms of resonance degree two to be meromorphically nonintegrable when the Jacobian matrices have a zero and pair of purely imaginary eigenvalues…

Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…

CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing…

The Poincare'-Dulac normal form of a given resonant system is in general non unique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this note we give an algorithm, based on the Lie algebraic…

We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a non-trivial adaptation of Deligne's method for the special case of ordinary schemes, are reasonably…

These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…

These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable systems covering the Arnold-Liouville theorem, inverse…

We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…

Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely…

This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…

Lecture notes from the Concentrated Graduate Course preceding the Workshop on Hodge Theory in String Theory at the Fields Institute in Toronto, November 11--15, 2013.

This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…

We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…

We study the structure of the solution sets in universal differential fields of certain differential equations of order two, the Poizat equations, which are particular cases of Li\'enard equations. We give a necessary and sufficient…