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Structures on Quantum Koszul Complexes

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If you have a question about this talk, please contact Joanna Fawcett.

Koszul complexes are well-known as computational tools in studying homological invariants, such as Hochschild and cyclic homology, of commutative algebras; deformed versions can play a similar role for families of non-commutative algebras such as quantum symmetric algebras and quantum tori. In the spirit of non-commutative geometry, we want to study the analogues of classical constructions, such as Gauss-Manin connections, Chern character maps and variations of Hodge structure, on cyclic homology, regarded as the non-commutative analogue of de Rham cohomology. In this talk, I’ll explain how one can derive explicit formulae for analogues of these structures on algebras with quantum Koszul complexes, and some concrete consequences of the calculations for understanding moduli of quantum tori.

This talk is part of the Junior Algebra and Number Theory seminar series.

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