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Homotopy Theory Seminar - Jens Jakob Kjaer

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November 16, 2017
11:30AM - 12:30PM
Math Tower 154

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Add to Calendar 2017-11-16 11:30:00 2017-11-16 12:30:00 Homotopy Theory Seminar - Jens Jakob Kjaer Title: The homology of algrebras over the spectral Lie operadSpeaker: Jens Jakob Kjaer (Notre Dame University)Abstract: One approach to computing homotopy groups of a space is using Goodwillie calculus. Calculus tells us that any simply connected space is the limit of a certain tower of fibrations, the Taylor tower, and we therefore have a spectral sequence computing the homotopy of the space. The first step in running this spectral sequence is computing the homology of the layers of the Taylor tower. Ching showed that the derivatives of the identity functor form an operad, called the Spectral Lie Operad. Behrens used this to equip the layers with certain power operations as well as a "Lie bracket" when we take coefficients in $\mathbb{Z}/2$, similar to how May recognized Dyer-Lashof operations coming from the E-infinity operad. A complete description of these structures was given by Antolin-Camarena. I will discuss the analogue for odd primes. I will in this talk describe the construction of the Dyer-Lashof-like operations and the "Lie-bracket", as well as the homology of the layers of the Taylor tower.Seminar URL: https://people.math.osu.edu/valenzuelavasquez.2/hts/ Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: The homology of algrebras over the spectral Lie operad

Speaker: Jens Jakob Kjaer (Notre Dame University)

Abstract: One approach to computing homotopy groups of a space is using Goodwillie calculus. Calculus tells us that any simply connected space is the limit of a certain tower of fibrations, the Taylor tower, and we therefore have a spectral sequence computing the homotopy of the space. The first step in running this spectral sequence is computing the homology of the layers of the Taylor tower. Ching showed that the derivatives of the identity functor form an operad, called the Spectral Lie Operad. Behrens used this to equip the layers with certain power operations as well as a "Lie bracket" when we take coefficients in $\mathbb{Z}/2$, similar to how May recognized Dyer-Lashof operations coming from the E-infinity operad. A complete description of these structures was given by Antolin-Camarena. I will discuss the analogue for odd primes. I will in this talk describe the construction of the Dyer-Lashof-like operations and the "Lie-bracket", as well as the homology of the layers of the Taylor tower.

Seminar URLhttps://people.math.osu.edu/valenzuelavasquez.2/hts/

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