Summer School in Mathematics Institut Fourier Grenoble

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Graduate Student Seminar Summer School in Mathematics, Institut Fourier, Grenoble June 16 { July 4, 2008 Duration of talks: 30 minutes Principal organizer: Evgeny Smirnov (Universitat Bonn) Gwyn Bellamy Representation theory of rational Cherednik algebras at t = 0 I will give an overview of the representation theory of the rational Cherednik algebras at t = 0 and show how much of this theory is governed by certain cuspidal representation, that I shall introduce. Lesya Bodnarchuk Simple vector bundles on degenerations of elliptic curves In my talk I discuss the problem of classication of simple coherent sheaves on certain degenerations of elliptic curves. Indecomposable vector bundles on smooth elliptic curves were classied in 1957 by Atiyah. An approach to study coherent sheaves on singular projective curves was suggested in works of Burban, Drozd and Greuel. In particular, it was shown that the category of coherent sheaves on a nodal cubic curve and on cycles of projective lines is tame, and all other degenerations of elliptic curves are wild. However, it turns out that all plane cubic curves are brick-tame. As a main technical tool to prove this result we use representation theory of boxes (dierential biquivers), worked out in 70s by the Kiev representation school to formalize and generalize the matrix problems. Martin Doubek Diagram cohomology via operads I will give elementary introduction to operads with emphasis on minimal models.

mckay correspodence

periodic components

diagram cohomology via operads

all constructions

representations along

product algebras

vector spaces

singularity inside

quiver representations

plane cubic curves

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pefav

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