What Is... Seminar
If you have a group acting on an algebraic variety, can you form a quotient variety? This is the question that Mumford sought to answer with geometric invariant theory (GIT). GIT is not so much a subject as a method which pops up all over the place in geometry. It's related to Hamiltonian dynamics on symplectic manifolds, it's used to construct many moduli spaces studied in algebraic geometry, and it is implicit in mathematical gauge theory and many of the mathematical subjects growing out of physics. I will give a brief overview of GIT and some cool applications to understanding the topology of spaces arising as quotients.