Apr

09

Dear all, James Mracek and myself are organizing a learning seminar on Geometric Invariant Theory in the summer term. GIT (Geometric Invariant Theory) is a powerful technique that was developed by Mumford in the 1960s to construct moduli spaces in algebraic geometry. Since then, GIT has emerged as not only an important tool in algebraic geometry, but also in symplectic geometry and arithmetic geometry. We plan to cover some subset of the following topics: - Different notions of quotients (categorical, good, geometric, etc) - Reductive Group Actions and Classical Invariant Theory (Hilbert's 14th problem, etc) - Linearization of group actions - Stability and numerical criterion for stability (Hilbert-Mumford criterion) - Construction of moduli spaces using GIT (moduli of quiver representations, moduli of genus g curves, etc) - GIT in symplectic geometry (GIT quotient vs symplectic quotient, Kahler/hyperkahler quotients; cf. Mumford Chapter 8) - GIT in arithmetic contexts (abelian schemes) We plan to use the following sources: - Dolgachev: Lectures in Invariant Theory - Mumford/Fogarty/Kirwan: Geometric Invariant Theory - Mukai: An Introduction to Invariants and Moduli I would like to have an organizational meeting for all those who are interested in attending this seminar. Please contact James (james.mracek@utoronto.ca) or myself (kl6@math.toronto.edu) if you are interested in attending so we can set up on potential meeting times. Also please feel free to make comments on choice of topics and sources. Thanks very much, Kevin

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