Juvitop Seminar
Fall 2017
This semester Juvitop will be about Goodwillie Calculus and the EHP Spectral Sequence.
We meet at 4:30 on Wednesday in 2151 unless otherwise noted.

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Andy Senger
In Juvitop this semester, we will study work of Behrens on the interaction between two ways of understanding the unstable homotopy groups of spheres: the EHP sequence and the Goodwillie tower of the identity. In this talk, I will outline some of the historical antecedents to this story and then give a brief overview of the main results of Behrens's work. I will also touch briefly on the interaction of this point of view with the chromatic approach to homotopy theory.
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 Kuhn Goodwillie towers and chromatic homotopy: an overview, sections 15
 Goodwillie, Calculus III: Taylor Series
 Lurie, Higher Algebra, sections 6.1.1  6.1.4
Introduction to Goodwillie Calculus
Peter Haine
References:
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Examples
Sanath Devalapurkar
Reference: Kuhn Goodwillie towers and chromatic homotopy: an overview, section 6
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The Goodwillie Tower of the Identity and the Unstable Periodic Homotopy of Spheres
Hood Chatham
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The Layers of the Goodwillie Tower of Spheres and Tits Buildings
Robert Burklund
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The Chain Rule and Operations on Layers of the Goodwillie Tower
Rasmus Johansen
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The Goodwillie Tower of the EHP sequence
Morgan Opie
Reference: The Goodwillie tower and the EHP sequence, section 2 and appendix A.1A.3
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The Goodwillie Filtration and the P map
Junho Fung
Reference: The Goodwillie tower and the EHP sequence, section 3
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Goodwillie differentials and Hopf invariants
To be determined
Reference: The Goodwillie tower and the EHP sequence, sections 4.14.5
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The Whitehead Conjecture
To be determined
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Exotic Goodwillie differentials and the geometric boundary effect
Andy Senger
Reference: The Goodwillie tower and the EHP sequence, sections 4.64.7 and appendix A.4
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Computing differentials in the EHP spectral sequence
To be determined
Reference: The Goodwillie tower and the EHP sequence, section 5
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Eva is live texing notes, which are available here: (pdf, tex)
This seminar is organized by Hood Chatham and Andy Senger.