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SUMMARY:GATP Seminar — Matt Booth (Imperial): Nonsmooth Calabi—Yau str
 uctures for algebras and coalgebras
DESCRIPTION:Calabi—Yau dg algebras are the derived-noncommutative analogu
 e of smooth Calabi—Yau varieties. I’ll talk about a generalised notion
  of Calabi-Yau structure for dg (co)algebras\, before giving a brief revie
 w of algebra-coalgebra Koszul duality\, and explaining why this `nonsmooth
  Calabi—Yau’ condition is dual to a symmetric Frobenius condition. The
 re is also an analogous one-sided version: Gorenstein (co)algebras are Kos
 zul dual to Frobenius (co)algebras. I’ll talk about a surprising example
 : commutative complete local Gorenstein k-algebras\, when equipped with th
 eir natural topology\, are pseudocompact Frobenius algebras. This is in so
 me sense a reflection of Matlis duality. As an application of the above th
 eory\, we obtain a new characterisation of Poincaré duality spaces\, whic
 h for simply connected spaces recovers Félix-Halperin-Thomas’s notion o
 f Gorenstein space. This is joint work with Joe Chuang and Andrey Lazarev.
URL:https://www.imperial.ac.uk/events/210595/gatp-seminar-matt-booth-imperi
 al-nonsmooth-calabi-yau-structures-for-algebras-and-coalgebras/
DTSTART;TZID=Europe/London:20260505T110000
DTEND;TZID=Europe/London:20260505T130000
LOCATION:Huxley 139\, Huxley Building\, South Kensington Campus\, Imperial 
 College London\, London\, SW7 2AZ\, United Kingdom
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