Related papers: Lectures on Foliation Dynamics: Barcelona 2010
These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent mathematical results about the long-time behaviour…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
These notes are based on an introductory minicourse on Poisson geometry given at CRM, Barcelona, in July 2022. They mostly contain foundational material, including motivating questions and key examples of Poisson structures, and highlight…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…
These are lecture notes of a course given in Pisa, SNS, in february 2002. They provide a classification of holomorphic foliations of nongeneral type on compact Kaehler surfaces.
The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed time-like distance. The importance of the foliation structure in the 2+1 dimensional model is studied…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
This lecture has the following sections: Systems and States; Brownian Motion; Segmental Relaxation and the Glass Transition; Dynamics of a Free Chain; Entanglement and Reptation. Appendices cover: Linear response theory, relaxation,…
These lectures provide a self-contained introduction to flux compactifications of type IIB string theory on Calabi-Yau orientifolds. The first lecture begins with geometric foundations, then presents vacuum solutions in Calabi-Yau…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
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…
This text grew out of some lecture notes prepared by the author in the occasion of a series of three lectures during the workshop "Young mathematicians in dynamical systems" organized by Francoise Dal'bo, Louis Funar, Boris Hasselblatt and…
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
We consider the problem of learning a manifold from a teacher's demonstration. Extending existing approaches of learning from randomly sampled data points, we consider contexts where data may be chosen by a teacher. We analyze learning from…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.
This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…
The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
This is a survey of recent results on manifolds with positive curvature from a series of lecture given in Guanajuato, Mexico in 2010. It also contains some hitsorical comments.