



Date 
Speaker 
Title and description 
Notes By: 
February 20 
Dylan Wilson 
The James construction.
James construction.
JamesMilnor splitting. Loopsuspensions.

Brief Overview
Notes

February 24 
Dylan Wilson 
Loop spaces.
Algebras over the little intervals operad. Segal's machine.
Bar construction.

Notes 
February 27 
Sean Pohorence 
Infinite loop spaces.
Segal's category. Ktheory.
BarratEccles, BarratPriddyQuillen, and Segal group completion.
The (false) transfer conjecture.

Notes 
March 3 
Maximilien Péroux 
Operads, approximation, and recognition.
Definition of E_nalgebras, and the theorems of May on approximation
and recognition. Twosided bar construction.


March 6 
Dylan Wilson 
Introducing power operations, and an extended example
We define the DyerLashof operations on E_inftyspaces and compute
how they act on one of our favorite infinite loop spaces BO.


March 10 
Aron Heleodoro 
Digression: Spectra and smash products.
Why is the smash product of spectra problematic? Survey of
solutions and models: symmetric spectra, EKMM, Smodules,
Kan's combinatorial spectra, etc.


March 13 
Yajit Jain 
Power operations and homology of configuration spaces.
Computation of homology of configuration spaces after F. Cohen.
Determination of algebraic structure on the homology of H_nspectra.


March 31 
Paul VanKoughnett 
The action of power operations on the dual Steenrod algebra.
Nishida formula, Steinberger's formula, HopkinsMahowald theorem, splitting theorems,
application to unoriented cobordism.


April 46 
N/A 
Problem session
Computing homology of some configuration spaces, and applying the Nishida theorem
in examples. Problems will be posted soon.


April 11 
Dylan Wilson 
Extended powers and Snaith splitting.
Definition of extended powers and some examples.
R. Cohen's proof of Snaith splitting. CohenMahowaldMilgram and
CohenCohenKuhnNeisendorfer. Indication of Mahowald family if there's
time. 

April 13 
Dylan Wilson 
Theorems of Toda and Nishida.
Hopkins's generalization of Nishida's second nilpotence
theorem. The Toda relation. Discussion of relationship
to DevinatzHopkinsSmith nilpotence theorem.


TBA 
Guchuan Li 
Operations in complex cobordism and Quillen's theorem.
Quillen's relationship between power operations in cobordism and
LandweberNovikov operations. Application to structure of complex
cobordism ring. 

TBA 
Paul VanKoughnett 
Operations in Ktheory and lambdaalgebras
Relationship between power operations in Ktheory and
lambdaalgebras. The padic version, thetaalgebras,
and McClure's theorem. K(1)local Einfinity rings and
a glimpse of GoerssHopkins obstruction theory.

