Actions of algebraic groups appear in many problems of Algebraic Geometry, encoding certain symmetries. Often one is interested in factoring out these symmetries and producing a new geometric object, a so-called quotient that parametrises the orbits of the action. In this framework, Geometric Invariant Theory (GIT) developed by David Mumford in 1965 deals with the problem of the existence of quotients, with an algebro-geometric structure, of an algebraic variety by the action of a reductive group. This method is extremely useful which also has important and surprising connections with symplectic geometry. In this lecture we shall give a gentle introduction to GIT construction, mainly focusing on the affine case. The algebraic side of this story is about finding the subalgebra of invariants (for an algebra with a group action) which dates back to Hilbert�s 14th problem.

Online via Zoom:
Meeting ID: 908 611 6889
Passcode: 362880