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SUMMARY:Structures on Quantum Koszul Complexes - Alexander Shannon (Univer
 sity of Cambridge)
DTSTART:20111028T130000Z
DTEND:20111028T140000Z
UID:TALK34115@talks.cam.ac.uk
CONTACT:Joanna Fawcett
DESCRIPTION:Koszul complexes are well-known as computational tools in stud
 ying homological invariants\, such as Hochschild and cyclic homology\, of 
 commutative algebras\; deformed versions can play a similar role for famil
 ies of non-commutative algebras such as quantum symmetric algebras and qua
 ntum tori. In the spirit of non-commutative geometry\, we want to study th
 e analogues of classical constructions\, such as Gauss-Manin connections\,
  Chern character maps and variations of Hodge structure\, on cyclic homolo
 gy\, regarded as the non-commutative analogue of de Rham cohomology. In th
 is talk\, I'll explain how one can derive explicit formulae for analogues 
 of these structures on algebras with quantum Koszul complexes\, and some c
 oncrete consequences of the calculations for understanding moduli of quant
 um tori.
LOCATION:MR4
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