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The current status of the application of hydrodynamics to ultrarelativistic heavy ion collisions is reviewed. We elaborate on the arguments for strong transverse flow and rapid thermalization and discuss future applications and trends in…
Lectures given at the CIMPA School "Geometrie sous-riemannienne", Beirut, Lebanon, 2012
A mini-conference on Hamiltonian and Lagrangian methods in fluid and plasma physics was held on November 14, 2002, as part of the 44th meeting of the Division of Plasma Physics of the American Physical Society. This paper summarizes the…
Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays,…
We briefly review recent developments of hydrodynamics, its gravitational description and relevance to relativistic heavy ion collisions. We discuss the basics of hydrodynamics, the fluid/gravity correspondence, triangle anomalies and…
Lecture notes delivered in Barcellona in the fall of 2003
These notes are based on a series of three lectures given at the Les Houches summer school on 'Integrability in Atomic and Condensed Matter Physics' in August 2018. They provide an introduction into the unusual transport properties of…
The problem of intermittency in developed hydrodynamic turbulence is considered. Explicit formulae taking into account effects of finite size of the inertial range are presented for the whole set of intermittency exponents. The formulae fit…
I summarize recent lattice results on QCD at finite temperatures and densities. Studies on the nature of the QCD transition at the physical point, continuum extra polations of thermodynamic quantities, and new calculations of hadronic…
The present overview and gentle introduction to Grassmannian calculus and some of its applications to probability collects the notes of a mini-course given by the authors at the Brazilian School of Probability, August 5-9, 2024, in…
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from…
Lectures at VII Jorge Andre Swieca Summer School in Nuclear Physics; Brasil; Jan 22 - Feb 4 1995. To be published by Plenum Press (C.A.Amaral Nunes ed.)
These are lecture notes for lectures at the Park City Math Institute, summer 2007. We cover aspects of the dimer model on planar, periodic bipartite graphs, including local statistics, limit shapes and fluctuations.
It is a working version of a lecture on the theory of enlargement of filtration, given at the African Mathematic School in Marrakech, October 19-23, 2015.
This presents an overview of relativistic hydrodynamic modeling in heavy-ion collisions prepared for Hot Quarks 2016, at South Padre Island, TX, USA. The influence of the initial state and viscosity on various experimental observables are…
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic…
Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions,…
This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
A new and very general technique for simulating solid-fluid suspensions has been described in a previous paper (Part I); the most important feature of the new method is that the computational cost scales with the number of particles. In…
These are the lecture notes (in Italian) of a course held in Perugia, Italy, during the summer 2002. They concern the basic facts on the iterative solution of linear systems. The course is self-contained and requires only basic knowledge of…