Welcome to the Algebra and Geometry Seminar at Iowa State University, organized by Jonas Hartwig, Jason McCullough, and Tathagata Basak.
During Fall 2024, the seminar runs on Thursdays at 3:10pm–4:00pm in Carver 401. Grad students are especially encouraged to attend.
Topics include:
The first meeting is a meet and greet where we introduce ourselves and share our interests.
Free resolutions are an essential technique in commutative algebra to study modules. Often free resolutions carry an algebra structure, turning it into a differential graded (DG) algebra. I will introduce DG algebras, survey known results, and define minimal models — i.e. how one creates a DG-algebra resolution even when the minimal free resolution carries no such structure.
To any local ring, one can associate a graded Lie algebra, called the homotopy Lie algebra. Useful properties of the ring can be encoded by properties of the Lie algebra (such as when the ring is a complete intersection, Golod, Koszul, etc.). I will introduce homotopy Lie algebras, compute a few examples, and highlight a few results in the literature.
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