I came across the book "Cohen-Macaulay Representations" by Graham J. Leuschke and Roger Wiegand, and now I'm wondering if this is an active area of research.
If yes, then



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> what are some of the active problems that people are interested in solving, and what connections does it have to other fields?
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Cohen-Macaulay Representations
Maximal Cohen-Macaulay modules, which seems to be at the center of this book, play a very important role in the theory of *non-commutative resolutions singularities*. Using MCM modules, Van-den-Bergh gave a very interesting reformulation of Bridgeland's proof of Bondal-Orlov conjecture in dimension 3. See [Three dimensional flops and non-commutative rings](https://arxiv.org/abs/math/0207170)


For more recent work, you can have a look at any recent paper by Amiot, Donovan, Iyama, Van-den-Bergh-Špenko, Wemyss and their collaborators on the subject.


