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SUMMARY:Harshit Yadav (Rice University\, USA)
DTSTART:20220704T140000Z
DTEND:20220704T150000Z
DTSTAMP:20260422T175959Z
UID:QGS/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QGS/64/">Fil
 tered Frobenius algebras in monoidal categories</a>\nby Harshit Yadav (Ric
 e University\, USA) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\
 nWe develop filtered-graded techniques for algebras in monoidal\ncategorie
 s with the goal of establishing a categorical version of Bongale's\n1967 r
 esult: A filtered deformation of a Frobenius algebra over a field is\nFrob
 enius as well. Towards the goal\, we construct a monoidal associated\ngrad
 ed functor\, building on prior works of Ardizzoni-Menini\, of Galatius et\
 nal.\, and of Gwillian-Pavlov. We then produce equivalent conditions for a
 n\nalgebra in a rigid monoidal category to be Frobenius in terms of the\ne
 xistence of categorical Frobenius form. These two results of independent\n
 interest are used to achieve our goal. As an application of our main\nresu
 lt\, we show that any exact module category over a symmetric finite\ntenso
 r category is represented by a Frobenius algebra in it. This is joint\nwor
 k with Dr. Chelsea Walton (Rice University)\n
LOCATION:https://researchseminars.org/talk/QGS/64/
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