Related papers: Causal Sets: Discrete Gravity (Notes for the Valdi…
Regression discontinuity designs are extensively used for causal inference in observational studies. However, they are usually confined to settings with simple treatment rules, determined by a single running variable, with a single cutoff.…
The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime…
This proceeding is based on a talk prepared for the XIV Marcel Grossmann meeting. We review some results on causal set inspired non-local theories as well as work in progress concerning their phenomenology.
Causal set theory offers a simple and elegant picture of discrete physics. But the vast majority of causal sets look nothing at all like continuum spacetimes, and must be excluded in some way to obtain a realistic theory. I describe recent…
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…
More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case…
The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos.…
Lecture notes on selected topics in the theory of gravitation.
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
These notes are the outgrowth of a series of lectures given at MSRI in January 1995 at the beginning of the special semester in complex dynamics and hyperbolic geometry. In these notes, the primary aim is to motivate the study of complex…
These notes are based on lectures presented at the 2001 Les Houches Summerschool ``Unity from Duality: Gravity, Gauge Theory and Strings''
In this paper we consider a claim that in the natural world there is no fact of the matter about the spatio-temporal separation of events. In order to make sense of such a notion and construct useful models of the world, it is proposed to…
This survey paper covers the breadth and depth of time-series and spatiotemporal causality methods, and their applications in Earth Science. More specifically, the paper presents an overview of causal discovery and causal inference,…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
Causal theory is now widely developed with many applications to medicine and public health. However within the discipline of reliability, although causation is a key concept in this field, there has been much less theoretical attention. In…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
These are notes for a graduate course in quantum gravity planned at IFT-UAM/CSIC for the spring term of 2020, but delayed for an indefinite period of time (although a shortened version was given in the Escuela de Fisica (Institute of…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
These are notes of a series of lectures on sieves, presented during the Special Activity in Analytic Number Theory, at the Max-Planck Institute for Mathematics in Bonn, during the period January--June 2002.