# Juvitop Seminar

## Fall 2017

In Fall 2017, Juvitop was about Goodwillie Calculus and the EHP Spectral Sequence.-
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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 1-5
- 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$\endgroup$ -
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#### The Goodwillie Tower of the Identity

### 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, chapter 2 and appendix A.1-A.3$\endgroup$ -
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#### The Goodwillie Filtration and the P map

### Junhou Fung

**Reference:**The Goodwillie tower and the EHP sequence, chapter 3$\endgroup$ -
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#### Goodwillie differentials and Hopf invariants

### Hood Chatham

**Reference:**The Goodwillie tower and the EHP sequence, sections 4.1-4.5$\endgroup$ -
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#### The Whitehead Conjecture

### Allen Yuan

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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$\endgroup$

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

This seminar was organized by Hood Chatham and Andy Senger.