Geometric Invariant Theory is concerned with answering the following problem: Given a group G acting on a projective variety X, how can we construct a quotient of X by the group action, and give it the structure of an algebraic variety? We cannot simply take the orbit space, and hope that this will be a variety, so it is important to throw out some bad (unstable) orbits from X, and identify some ok (semistable) orbits together in the quotient. In this talk, I will show how to construct this quotient abstractly, and introduce the remarkable Hilbert-Mumford numerical criterion, which allows us to determine which orbits in X are stable, semistable and unstable, and therefore what our quotient looks like geometrically. In part 2 next week, I will show how I am applying GIT to my research.
Introduction to Geometric Invariant Theory part 1
Thu, Sep. 25 2:30pm (MATH 3…
Functional Analysis
Various
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The members of the functional analysis group will give short talks introducing their research.
TBA