Related papers: IMPANGA lecture notes on log canonical thresholds
We describe a systematic method for complete enumeration of configuration classes (CCs) of the spin-1/2 Ising model in the energy-magnetization plane. This technique is applied to the antiferromagnetic Ising model in an external magnetic…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely many steps.
These lecture notes introduce the reader to the hot big bang model, cosmological perturbations, gravitational waves, the cosmic microwave background, inflation, the singularity problem, the cosmological constant problem and the cosmology of…
These lecture notes are organized into ten lessons that summarize the status of inflationary cosmology.
We review some elementary aspects of the critical properties of the series of metal-insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being…
This lecture is an introduction to cosmological tests with clusters of galaxies. Here I do not intend to provide a complete review of the subject, but rather to describe the basic procedures to set up the fitting machinery to constrain…
We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
An elementary, pedagogical introduction to the large-N limit of QCD and to its phenomenological implications is presented, and a survey of lattice results in the 't Hooft limit is briefly discussed.
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.
Some elementary rigorous remark about the replica formalism in the Statistical Physics' approach to threshold phenomena in Computational Complexity Theory is presented.
In order to guide teaching practices in Initial and Primary Education (IPE) level, it seems fundamental to start with an epistemological and didactic analysis of the programmatic content of the Knowledge of Nature area in the curriculum…
For any system with limited statistical knowledge, the combination of evidence and the interpretation of sampling information require the determination of the right reference class (or of an adequate one). The present note (1) discusses the…
Some points concerning the relation of strings to interfaces in statistical systems are discussed.
We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.
We show the finiteness of log pluricanonical representations under the assumption of the existence of a good minimal model.
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely…
This review presents an introduction to Quantum Cosmology, including the mathematical methods essential to the canonical approach, some of the existing conceptual problems and the connection of the models to possible observables.