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SUMMARY:Semisimple Field Theories and Stable Diffeomorphisms
DTSTART:20211109T141500
DTEND:20211109T151500
DTSTAMP:20260510T110226Z
UID:31ab944fcd7b3e0e21118d078200d2eb16bdce2751fc80549ac252ec
CATEGORIES:Conferences - Seminars
DESCRIPTION:David Reutter\, Max-Planck-Institut für Mathematik\nA major o
 pen problem in quantum topology is the construction of a 4-dimensional top
 ological field theory (TFT) in the sense of Atiyah-Segal which is sensitiv
 e to exotic smooth structure. More generally\, how much manifold topology 
 can a TFT see? \n\nIn this talk\, I will outline an answer to this questi
 on for even-dimensional `semisimple’ TFT: \nSuch theories can at most s
 ee the stable diffeomorphism type of a manifold and conversely\, if two su
 fficiently finite manifolds are not stably diffeomorphic\, then they can b
 e distinguished by a semisimple field theory. In this context\, `semisimpl
 icity' is a certain algebraic condition satisfied by all currently known e
 xamples of linear algebraic TFT in more than two dimensions\, and two 2n-m
 anifolds are said to be stably diffeomorphic if they become diffeomorphic 
 after connected sum with sufficiently many copies of S^n x S^n.\n\nAlong t
 he way\, I will introduce a number of semisimple TFTs built from homotopy 
 types acted on by the orthogonal group O(n)\, and will discuss various imp
 lications\, such as the fact that 4d oriented semisimple TFT cannot see sm
 ooth structure\, while unoriented ones can. \n\nThis is based on arXiv:20
 01.02288 and joint work in progress with Christopher Schommer-Pries.
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012 https://epfl.zo
 om.us/j/94351048760
STATUS:CONFIRMED
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