An introduction to matrix factorisations Part 1


Abstract: In the seminar we have already heard about Landau-Ginzburg models, potentials, and cohomological field theories associated to singularities by Fan-Jarvis-Ruan-Witten and Polishchuk-Vaintrob. Central to this story are matrix factorisations, and over two talks I will give an introduction to their theory, starting from scratch. I will begin with a brief introduction to singularity theory, define matrix factorisations and their categories (including variants such as graded and equivariant matrix factorisations) and state the basic theorem due to Buchweitz-Orlov which relates matrix factorisations to maximal Cohen-Macaulay modules and to a Verdier quotient of the bounded derived category of coherent sheaves on a singular algebraic variety. Much of the time will be devoted to just working carefully through the details in the case of A_n singularities.

In Part 2 I will explain how the classification of simple singularities fits into an ADE pattern, and how the McKay correspondence classifies matrix factorisations of these ADE singularities in terms of representations of finite subgroups of SL(2,C).

Zoom info.

Tech notes: the format of the talk is experimental, in the sense that I will deliver it using an iPad Pro whose screen is shared through Zoom. Participants should keep their microphones muted unless they wish to ask a question (and please do ask questions).

I believe I have correctly scheduled a Zoom session for tomorrow at 11am, that people can join with the URL below.

Daniel Murfet is inviting you to a scheduled Zoom meeting.

Topic: LG/CohFT seminar Time: Mar 18, 2020 11:00 AM Australia/Melbourne

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  •  Daniel Murfet
    Daniel Murfet, University of Melbourne