Intended audience - Advanced Masters’s students and higher.
Short DescriptionRight from its introduction by Hamilton in 1982, the Ricci flow has found applications in both geometryand topology. Perhaps the crowning achievement of the Ricci flow is the proof of the Poincaré conjectureor more generally the proof of the Thurston’s Geometrization conjecture by Perelman. This courseintends to be an introduction to the Ricci flow and to study many of its properties and applications.The target audience is advanced Bachelors and Masters’s students and PhD students so only basicknowledge of Riemannian geometry and analysis (especially PDEs) will be very beneficial. A detailed(preliminary) discussion of topics is outlined below. If the response will be good, then there could alsobe a "Part 2" of the course which probably will cover those results of Perelman which won’t be coveredin the first part.