Abstract: The aim of this talk is to introduce the two notions of free resolutions and Koszul algebras, give some important examples of such objects, and motivate why they might be interesting to a general mathematical audience. We will then put everything together to discuss what can be said about the free resolutions of Koszul algebras and progress towards answering a question of Avramov, Conca, and Iyengar about the Betti numbers of Koszul algebras. This talk should be very accessible to graduate students.
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