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The iTHEMS Math seminar was held on 4 December, inviting Wahei Hara from Waseda university. The title of the talk was “Noncommutative crepant resolutions and some higher dimensional flops”. The central topic was singularities of algebraic varieties and representation theory.
In the first part, the speaker explained the McKay correspondence as an example of connections between du Val singularities and representation theory of finite subgroups of the special linear group of degree two over the complex number field.
In the second part, the speaker talked about noncommutative crepant resolutions of singularities. There are several ways to interpret the Mckay correspondence. The derived McKay correspondence is the interpretation of the McKay correspondence in terms of derived categories. The notion of noncommutative crepant resolutions is the generalization of the derived McKay correspondence to a large class of singularities. We discussed applications of noncommutative resolutions to the study of derived categories in birational geometry.