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I was wondering what are some of the hot topics in quiver representation or representation theory of algebras that can lead to good mathematics and is important to many mathematicians and top mathematicians?

I'm not looking for exact question or anything but more like an overview/idea of some topics. For e.g.- quiver varieties, tau-tilting theory, etc.

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    $\begingroup$ I'm afraid this is really too broad for a helpful answer; have you looked at en.wikipedia.org/wiki/List_of_representation_theory_topics $\endgroup$
    – Carlo Beenakker
    Commented Aug 23, 2021 at 8:23
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    $\begingroup$ @CarloBeenakker: I don't think that list is very helpful for outlining possible directions for research topics. It is mostly a list of standard textbook topics, which are very different from the directions in which research is moving. $\endgroup$
    – Ben McKay
    Commented Aug 23, 2021 at 8:50
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    $\begingroup$ It's 15 years old at this point, but maybe this book is interesting to you?: "Trends in Representation Theory of Algebras and Related Topics," bookstore.ams.org/conm-406 $\endgroup$
    – Sam Hopkins
    Commented Aug 23, 2021 at 13:12

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One of the best way to learn what is hot is to attend conferences and be in touch with people in the field. The new homepage https://fdlist.math.uni-bielefeld.de/t/welcome-to-fdlist/21 contains a lot of information including a list of all related conferences.

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A starting point is the MSC2020 database. The codes 16G20 and 16G70 are directly related to quivers. Now you can look up recent papers on MathSciNet or zbMATH (subscription required).

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    $\begingroup$ Subscription is required for MathSciNet, but not for zbMath. $\endgroup$
    – Zach Teitler
    Commented Aug 24, 2021 at 11:52

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