Fall 2017

In Fall 2017, Juvitop was about Goodwillie Calculus and the EHP Spectral Sequence.

• • Sep 202017
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  Overview

  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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• • Sep 272017
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  Introduction to Goodwillie Calculus

  Peter Haine

  Notes

  References:

  • Kuhn Goodwillie towers and chromatic homotopy: an overview, sections 1-5
  • Goodwillie, Calculus III: Taylor Series
  • Lurie, Higher Algebra, sections 6.1.1 - 6.1.4
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• • Oct 042017
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  Examples

  Sanath Devalapurkar

  Notes

  Reference: Kuhn Goodwillie towers and chromatic homotopy: an overview, section 6

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• • Oct 112017
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  The Goodwillie Tower of the Identity

  Hood Chatham

  Notes (source)

  Reference: Arone-Mahowald, The Goodwillie tower of the identity and the unstable periodic homotopy of spheres

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• • Oct 182017
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  The Layers of the Goodwillie Tower of Spheres and Tits Buildings

  Robert Burklund

  Reference: Arone-Dwyer, Partition complexes, Tits buildings, and symmetric products.

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• • Oct 252017
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  The Chain Rule and Operations on Layers of the Goodwillie Tower

  Rasmus Johansen

  References:

  • Behrens, The Goodwillie tower and the EHP sequence, chapter 1
  • Ching, Bar constructions for topological operads and the Goodwillie derivatives of the identity
  • Arone-Ching, Operads and chain rules for the calculus of functors
  • Lurie, Higher Algebra, Section 6.3
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• • Nov 012017
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  The Goodwillie Tower of the EHP sequence

  Morgan Opie

  Reference: The Goodwillie tower and the EHP sequence, chapter 2 and appendix A.1-A.3

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• • Nov 082017
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  The Goodwillie Filtration and the P map

  Junhou Fung

  Notes

  Reference: The Goodwillie tower and the EHP sequence, chapter 3

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• • Nov 152017
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  Goodwillie differentials and Hopf invariants

  Hood Chatham

  Notes

  Reference: The Goodwillie tower and the EHP sequence, sections 4.1-4.5

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• • Nov 292017
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  The Whitehead Conjecture

  Allen Yuan
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• • Dec 062017
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  Exotic Goodwillie differentials and the geometric boundary effect

  Andy Senger

  Reference: The Goodwillie tower and the EHP sequence, sections 4.6-4.7 and appendix A.4

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Eva is live texing notes, which are available here: (pdf, tex)

This seminar was organized by Hood Chatham and Andy Senger.