West Coast Algebraic Topology Summer School

  • Start Date: 07/16/2012
  • End Date: 07/21/2012
Lectures will be given by participants as well as the organizing committee. Please indicate your willingness to give a lecture in the form below.

Stanford University

The scientific goal is to provide a modern introduction to algebraic K-theory, with the aim of bringing participants to the research frontier. In particular,the workshop will focus on


  • the current understanding and interpretation of the construction, functoriality, and multiplicative structures on the algebraic K-theory spectrum,
  • trace methods for computing via comparison to TC and THH,
  • Rognes' program to understand K(S) and localization phenomena, and
  • an exploration of the modern applications of the algebraic K-theory of brave new rings to the topology of manifolds.

This summer school is aimed at graduate students and post-docs, though all are welcome. We have support from the National Science Foundation for at least forty student/post-doc participants, including local accommodations and partial reimbursement of travel expenses (depending on interest and available funds). The Pacific Institute for the Mathematical Sciences will support travel by Canadian students.


Format: some participants will be preparing and giving lectures which have been planned in advance by the scientific committee.  The number of lectures each day will be limited, and the additional time used for activities to complement lectures. Some possible activities could be: question sessions; students working on problems; smaller lectures which could fill in background for less experienced participants or go further into recent advances for more experienced participants; reading or side discussions.


There is no registration fee for this event, but we ask all who are interested in coming to complete the form below so that we may plan accordingly and create a conference mailing list.


Please note that the deadline for applications requesting financial support is April 15, 2012. Offers will be made after that date.

Abstracts / Downloads / Reports: 

All lectures will be in room 380-C in the Stanford Math Department. Space for questions, exercises, reading and other discussion during the indicated times (and others) include rooms 380-W and 380-X in addition to 380-C.



  • 8:40 I1 - Introduction
  • 10:00 M1 - Lower K-theory of manifolds
  • 12:30 pm - Questions and Exercises
  • 2pm I2 - Construction of Algebraic K-theory
  • 3:30 I3 - Fundamental Theorems
  • 5 pm - Questions and Exercises


  • 9 - Organizers
  • 9:20 I4 - The approximation theorem
  • 10:50 I5 - The K-theory of algebraically closed and finite fields
  • 2 - Questions and Exercises
  • 4 M2 - Pseudoisotopies and K2
  • 8 - Questions and Exercises


  • 9 - Organizers
  • 9:20 T1 - THH, TC and the Cyclotomic Trace
  • 10:50 T2 - Computations in THH and TC
  • Free afternoon


  • 9 - Organizers
  • 9:20 M3 - Waldhausen's work
  • 10:50 M4 - Outline of the proof of Waldhausen's splitting theorem
  • 2 - Questions and Exercises
  • 4 M5 - Higher Riemann-Roch theory, higher Reidemeister torsion
  • 8 - Questions and Exercises


  • 8:40 Organizers
  • 9 T3 - The De Rham- Witt complex
  • 10:30 T4 - On the K-theory of local fields
  • 1 - Questions and Exercises
  • 2:30 T5 - The algebraic K-theory of topological K-theory and the chromatic tower for the algebraic K-theory of a point
  • 4 - Questions and Exercises


  • 10 - Organizers Wrap-up

Scientific committee



Andrew Blumberg

Bill Dwyer

Teena Gerhardt

John Klein

Mike Mandell


Organizing committee


Alejandro Adem

Ralph Cohen

Dev Sinha

Other Information: 
Registration for this event is now closed. Thank you for your interest.