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Abstract:
This is a joint work with Joe Chuang. We describe a combinatorial setting
for tilting theory for Calabi-Yau algebras. We view them as "non-commutative
local Calabi-Yau manifolds" and tilting corresponds to a non-commutative
birational transformation involving a "compact" exceptional locus. A typical
example is provided by the orbifold quotient of n-dimensional space by a finite
subgroup of SLn acting freely outside the origin.
These combinatorics are related to the topology of the space of stability
conditions of the derived category. In dimension 3, the combinatorics are
related to cluster mutations.
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