Related papers: The study of translational tiling with Fourier Ana…

This talk is dedicated to various aspects of Mirror Symmetry. It summarizes some of the mathematical developments that took place since M. Kontsevich's report at the Z\"urich ICM and provides an extensive, although not exhaustive,…

This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure,…

These are the informal notes of two seminars held at the Universita` di Roma "La Sapienza", and at the Scuola Normale Superiore in Pisa in Spring and Autumn 1997. We discuss in detail the content of the parts of Givental's paper dealing…

These are lecture notes from author's mini-course during Session 1: "Vertex algebras, W-algebras, and application" of INdAM Intensive research period "Perspectives in Lie Theory", at the Centro di Ricerca Matematica Ennio De Giorgi, Pisa,…

Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools, do not necessarily understand…

This manuscript presents shortly the results obtained by participants of the scientific seminar which is held more than twenty years under leadership of the author at Donetsk University. In the list of references main publications are…

This paper contains the notes of lectures on the theory of interlayer exchange coupling presented at the 30-th Ferienschule of the Institut fuer Festkoerperforschung, Forschungszentrum Juelich, March 1999.

This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…

Notes of an introductory course given at the conference "Torsors: Theory and Applications" in Edinburgh, January 2011.

This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.

Lectures presented at the Spring School, Trieste, Italy 1993.

This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…

These pages covers my expository talks during the seminar "Sub-Riemannian geometry and Lie groups" organised by the author and Tudor Ratiu at the Mathematics Department, EPFL, 2001. However, this is the first part of three, in preparation,…

The nonlinear Fourier transform discussed in these notes is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of…

This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.

These are notes from a 3-lecture course given by V. Dokchitser at the ICTP in Trieste, Italy, 1st--5th of September 2014, as part of a graduate summer school on "L-functions and modular forms". The course is meant to serve as an…

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…

The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…

This is a review (including some background material) of the author's work and related activity on certain exactly solvable statistical models in two dimensions, including the six-vertex model, loop models and lozenge tilings. Applications…