This is a website to organize the 2017 Pre-Talbot Seminar at Northwestern. We meet at 12 noon on Mondays and Fridays in Annenberg G28.
The mailing list. If your name does not appear below, you are not on the mailing list:
  1. Araminta Amabel
  2. Aron Heleodoro
  3. Brian Williams
  4. Catherine Ray
  5. Foling Zou
  6. Grigory Papayanov
  7. Guchuan Li
  8. Guillermo Tochi
  9. Johan Konter
  10. Lauren Bandklayder
  11. Maximilien Péroux
  12. Nilay Kumar
  13. Nir Avni
  14. Paul VanKoughnett
  15. Pax Kivimae
  16. Sam Nariman
  17. Sean Pohorence
  18. Spencer Liang
  19. Yajit Jain
Date Speaker Title and description Notes By:
February 20 Dylan Wilson The James construction. James construction. James-Milnor splitting. Loop-suspensions. 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. K-theory. Barrat-Eccles, Barrat-Priddy-Quillen, and Segal group completion. The (false) transfer conjecture. Notes
March 3 Maximilien Péroux Operads, approximation, and recognition. Definition of E_n-algebras, and the theorems of May on approximation and recognition. Two-sided bar construction.
March 6 Dylan Wilson Introducing power operations, and an extended example We define the Dyer-Lashof operations on E_infty-spaces 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, S-modules, 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_n-spectra.
March 31 Paul VanKoughnett The action of power operations on the dual Steenrod algebra. Nishida formula, Steinberger's formula, Hopkins-Mahowald theorem, splitting theorems, application to unoriented cobordism.
April 4-6 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. Cohen-Mahowald-Milgram and Cohen-Cohen-Kuhn-Neisendorfer. 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 Devinatz-Hopkins-Smith nilpotence theorem.
TBA Guchuan Li Operations in complex cobordism and Quillen's theorem. Quillen's relationship between power operations in cobordism and Landweber-Novikov operations. Application to structure of complex cobordism ring.
TBA Paul VanKoughnett Operations in K-theory and lambda-algebras Relationship between power operations in K-theory and lambda-algebras. The p-adic version, theta-algebras, and McClure's theorem. K(1)-local E-infinity rings and a glimpse of Goerss-Hopkins obstruction theory.

Links


The 2017 Talbot Workshop