The chair of algebraic geometry is a research group doing research in algebraic geometry in general. It is an organizational entity, which is part of the Institute of Mathematics at EPFL.
The goal of algebraic geometry is to understand geometrically common zero sets of multivariable polynomials. The latter objects are addressed by different names, such as, algebraic sets, varieties, schemes, etc., depending on the abstractness of the given setup. Let us use here the frendliest one: algebraic sets. Algebraic sets being such fundamental and natural objects, it is hard to attach a single date to the start of the history of algebraic geometry. There were certainly traces of it appearing in ancient Greeks’ mathematics, and as approaching the present, one can find more and more related ideas on a language closer and closer to the currently used one.
The main focus of the chair of algebraic geometry is the classification theory of algebraic sets. As in many branches of mathematics it is also essential in algebraic geometry to have a good classification theory of the basic objects of the field. This then can be applied to solve different problems in the field, or in other related fields such as arithmetic or complex geometry. The main goal of the chair is to further advance the classification theory, as well as to extend the list of the latter applications.