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DTSTART;TZID=America/New_York:20251009T140000
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DTSTAMP:20260508T072250
CREATED:20250911T184457Z
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SUMMARY:Profinite tensor powers
DESCRIPTION:Algebra Seminar \nSpeaker: David Treumann (Boston College) \nTitle: Profinite tensor powers \nAbstract: I’ll discuss the problem of defining a tensor product of profinitely many copies of a vector space V\, and propose a definition $\bigotimes_X^{mcc} V$ in the special situation that (1) V is finite-dimensional over F_2\, and (2) the profinite X indexing the tensor factors is acted on with finitely many orbits by a pro-2-group. The “mcc” on the tensor sign stands for “magnetized and conditionally convergent.” A variant construction makes sense when V is a bimodule over a semisimple F_2-algebra\, and the index set X has the profinite version of a cyclic order. The definition organizes some computations in Heegard Floer homology: it can be pitched as a computation of the HF of some pro-3-manifolds\, though we do not know how to define such a thing. This is joint work with CM Michael Wong. \n 
URL:https://cmsa.fas.harvard.edu/event/algebra-seminar_10925/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebra Seminar
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