Reading Seminar:
Geometric Invariant Theory and Nakajima's Quiver Varieties
The seminar takes place on Fridays from 10am - 12am in the seminar room at the MPIM.
List of talks:
The current distribution of talks is given below.
Invariant Theory:
1. Classical Invariant Theory: Marc
  Goal: Present examples of classical invariant theory of matrices and quiver representations, [Schmitt, Section 1.3]
2. Quotients: Thorge
  Goal: Definition and Constructions of quotients, [Schmitt, Section 1.4]
3./4. Stability and Hilbert-Mumford Criterium: Jacinta / Joanna
  Goal: Definition of stability and proof of the criterium, [Schmitt, Section 1.5.1]
5. Quiver Moduli: Gustavo
  Goal: Present quiver moduli following King, [Schmitt, Section 1.5.1], [King]
6. Classical Moduli Problems: Hans
  Goal: Explain one or two classcial moduli problems, [Mumford, Chapter 4]
Quiver Varities:
7. Symplectic Geometry: David
  Goal: Explain hamiltonian reduction and relation to GIT quotients, [Ginzburg, Section 4.1], [Kirwan, Chapters 6-8]
8. Lusztig's Quiver Varieties I: Johannes
  Goal: Explain definitions and first properties, see Theorem 4.5.6 in Ginzburg, [Ginzburg, Section 4.2-4.5]
9. Lusztig's Quiver Varieties II: Catharina / Sheng
  Goal: Explain the construction of quantum groups using quiver varieties, [Lusztig]
10./11. Nakajima's Quiver Varieties I: Bea / Arik
  Goal: Explain definitions and first properties, see Theorem 5.2.2 in Ginzburg, [Ginzburg, Section 5.1-5.3]
12. Nakajima's Quiver Varieties II: Dyhan
  Goal: Explain the construction of the lagrangian subvarieties and their properties, [Ginzburg, Section 5.4]
13. Convolution: Tomasz
  Goal: Explain convolution both of functions and Borel-Moore homology, [Ginzburg, Section 6]
14. Nakajima's Quiver Varieties III: Michael
  Goal: Explain constructions of Lie algebras and highest weight modules using quiver varieties, [Ginzburg, Section 7]
References:
The following is a list of references for the seminar.
[Ginzburg] V. Ginzburg, Lectures of Nakajima's Quiver Varieties
[King] A.D. King, Moduli of Representations of Finite Dimensional Algebras
[Kirwan] F.C. Kirwan, Cohomology of Quotients in Symplectic and Algebraic Geometry
[Lusztig] G. Lusztig, Constructible functions on varieties attached to quivers
[Schmitt] A.H.W. Schmitt, Geometric Invariant Theory and Decorated Principal Bundles
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