Lectures on minimal models

Lectures on the Log Minimal Model Program

We explain the fundamental theorems for the log minimal model program for log canonical pairs.

Topic class on minimal surfaces — lectures by Rick Schoen

This series of lecture notes were taken for the topic class on minimal surfaces given by Professor Rick Schoen in the Winter quarter of 2012 at Stanford. We kept the pace of these lectures by dates. These lectures start from basic materials on minimal surfaces, e.g. first and second variations, and monotonicity formulae, and then discuss several curvature estimates for minimal surfaces. Afterwa...

On Minimal Finite Models

A minimal finite model of a topological space is the smallest finite topological space that is weakly homotopic to that particular space. So far, we have only found literatures on the minimal finite models for spheres and finite graphs, and they are concluded in Barmak and Minian’s paper [1]. In this paper, we will take a look at these minimal finite models and push our scope a bit further to m...

Lectures

COSMOLOGICAL MODELS Cargèse Lectures 1998

The aim of this set of lectures is a systematic presentation of a 1 + 3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1 + 3 covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Cargèse lectures [7], but they then go on to give (ii) t...