Related papers: Fredholm Operators and Spectral Flow
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout…
Lectures presented at the 42nd Scottish Universities Summer School in Physics, St. Andrews, Scotland, August 1993.
This is the introductory part of my Ph.D thesis, defended at the Faculty of Science and Technology, NTNU on December 10, 2012.
Proceedings of the international Workshop on ``Dynamics and Thermodynamics of Blackholes and Naked Singularities``, that took place at the Department of Mathematics of the Politecnico of Milano from 13 to 15 May 2004.
Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
The problem of Monte-Carlo method study at computer simulation lessons in a Teachers' Training Institute is reviewed in the article. The suggested technique envisages the simulation modelling of various stochastic processes. They include…
We give an account of the main achievements of the scientific career of Andrea Vitturi so far, that have recently been discussed during the workshop "Theoretical Nuclear Physics in Padova" on the occasion of his retirement from full…
These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…
These are lecture notes of a course on Calogero-Moser systems and their connections with representation theory and geometry, given by the author in Zurich in May-June 2005.
This text describes the content of the Takagi lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for boolean functions and its application to the study of phase transitions in…
We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compute Fredholm indices via a generalized spectral flow, using…
These notes have been prepared as reading material for the mini-course that the author gave at IMS, National University of Singapore, as part of the "Summer school on the moduli space of Higgs bundles".
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
Lecture notes of a short course on geometric control theory given in Brasov, Romania (August 2018) and in Jyv\"askyl\"a, Finland (February 2019).
The article is a lightly edited version of my habilitation thesis at the University Wuerzburg. My aim is to give a self contained, if concise, introduction to the formal methods used when off-line learning in feedforward networks is…
Brief review of the recent progress in semiconductor spintronics (theory and experiment) and the current theoretical problems in it is presented. Invited paper at the 2006 Advanced Research Workshop "Future Trends in Microelectronics: Up to…
A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.