Related papers: A swift introduction to holomorphic foliations wit…
We classify singular foliations admitting a given leaf and a given transverse singular foliation.
The goal of these lecture notes is to introduce the developing research area of gravitational-wave phenomenology. In more concrete terms, they are meant to provide an overview of gravitational-wave sources and an introduction to the…
We study codimension one smooth foliations with Morse type singularities on closed ma-nifolds. We obtain a description of the manifold in case the number of centers in greater then the number of saddles. This result relies on and extends…
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…
These lecture notes are meant to serve as an introduction to some geometric constructions and techniques (in particular the ones of toric geometry) often employed by the physicist working on string theory compactifications. The emphasis is…
These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
A singular foliation $\mathcal F$ gives a partition of a manifold $M$ into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space $M / \mathcal…
These are expanded notes for a short series of lectures, presented at the University of Luxembourg in 2017, giving an introduction to some of the ideas of supersymmetry and supergeometry. In particular, we start from some motivating facts…
This is a note on toroidalization, formulated as the problem of resolution of singularities of morphisms in the logarithmic category. It is submitted to the proceedings of the Barrett conference held at the University of Tennessee at…
This note is an expository account of the theory of staggered sheaves, based on a series of lectures given by the author at RIMS (Kyoto) in October 2008.
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus,…
These are the notes for a lecture series on Heegaard Floer homology, given by the first author at the R\'enyi Institute in January 2023, as part of a special semester titled ``Singularities and Low Dimensional Topology''. Familiarity with…
This is a revision of some expository lecture notes written originally for a 5-hour minicourse on the intersection theory of punctured holomorphic curves and its applications in 3-dimensional contact topology. The main lectures are aimed…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
This article, written for undergraduate mathematics students, provides an accessible introduction to a few key problems in tiling theory: Heesch's problem, the isohedral number problem, and the existence of an aperiodic monotile. I…
A smooth foliation is Riemannian when its leaves are locally equidistant. The closures of the leaves of a Riemannian foliation on a simply connected manifold, or more generally of a Killing foliation, are described by flows of transverse…
Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities.…
These notes originated in a series of lectures I gave in Marseille in May, 2013. I was invited to give an introduction to the isomorphism theorems, originating with Dynkin, which connect Markov local times and Gaussian processes. This is an…
This article discusses questions in one and several complex variables about the size of the sum of the moduli of the terms of the series expansion of a bounded holomorphic function. Although the article is partly expository, it also…