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SUMMARY:Algebraic patterns and additivity of equivariant little disk opera
 ds [MPIM]
DTSTART:20261027T100000Z
DTEND:20261027T113000Z
DTSTAMP:20261030T013100Z
UID:indico-event-1678@math-events.uni-bonn.de
DESCRIPTION:Speakers: Natalie Stewart (MPIM)\n\nAbstrakt homotopy theory s
 eminar \nIn the equivariant algebraic topology surrounding manifolds with
  smooth $G$-action\, Pontryagin-Thom techniques demand we study "$V$-loop 
 spaces\," where $V$ is a real $G$-representation. Moreover\, in finite-gro
 up-equivariant higher algebra\, these are corpresentable as suitably group
 like algebras over a "$G$-operad" called $\\mathbb{E}_V$\; in this talk\, 
 I will discuss some aspects of how to construct an equivalence to the cate
 gory of objects with coherently interchanging $\\mathbb{E}_V$-algebra and 
 $\\mathbb{E}_W$-algebra structures from the category of $\\mathbb{E}_{V \\
 oplus W}$-algebras.\nThis aformentioned $(\\infty\,2)$-category of $G$-ope
 rads turns out to be presented as the "fibrous patterns" associated with a
 n "algebraic pattern\," generalizing the passage from $\\mathrm{Fin}_* = \
 \Gamma^{\\mathrm{op}}$ to the $(\\infty\,2)$-category of operads. In this 
 talk\, I will more precisely describe a rich Morita theory of suitably nic
 e fibrous patterns\, and indicate how to use it to reduce the above additi
 vity theorem to elementary manifold topology. \n \n\nhttps://math-events
 .uni-bonn.de/event/1678/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1678/
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