Spring School on Algebraic Topology

The first meeting of Spring School on Algebraic Topology was held in March 2013 at Faculty of Science, Shinshu University. The main theme for the first meeting was ``spectral sequence'', which is one of the most fundamental computational tools in algebraic topology. Yes. We compute spectral sequences in algebraic topology. On the other hand, spectral sequences are used as a tool to aid proofs in other areas such as algebraic geometry. There will be ``how to'' talks on important spectral sequences used in algebraic topology.
  • Date: March 8, 9, and 10, 2013
  • Venue: Department of Mathematical Sciences, Shinshu University
  • Talks:
    1. The idea of spectral sequences (Dai Tamaki, Shinshu University)
    2. Serre and Atiyah-Hirzebruch spectral sequences (Tetsu Nishimoto, Kinki Helth Welfare University)
    3. Eilenberg-Moore spectral sequences (Katsuhiko Kuribayashi, Shinshu University)
    4. Bockstein spectral sequence (Dai Tamaki, Shinshu University)
    5. Adams-type spectral sequences (Hirofumi Nakai, Tokyo City University)
    6. Problem session
  • Lecture notes: Here is a collection of lecture notes in Japanese.
  • Schedule:
    • March 8th
      • 13:30-14:50 The idea of spectral sequences (1) "How to construct spectral sequences" (Tamaki)
      • 15:10-16:10 The idea of spectral sequences (2) "What do spectral sequences compute?" (Tamaki)
      • 16:30-17:00 Self-introduction by participating students
    • March 9th
      • 9:30-10:50 Serre spectral sequence and Atiyah-Hirzebruch spectral sequence (1) "Let's compute anyway" (Nishimoto)
      • 11íž10-12:30 Serre spectral sequence and Atiyah-Hirzebruch spectral sequence (2) "Relations between differentials and cohomology operations" (Nishimoto)
      • 14:00-15:15 Eilenberg-Moore spectral sequence (1) "Two Eilenberg-Moore's and their friends" (Kuribayashi)
      • 15:30-16:30 Eilenberg-Moore spectral sequence (2) "Operators, or helpers for computations" (Kuribayashi)
      • 16:50-18:00 Bockstein spectral sequence "Nobody knows Bockstein Lemma" (Tamaki)
      • 19:00- Welcome party
    • March 10th
      • 9:30-10:30 Problem session
      • 10:30-10:45 Group photo
      • 10:45-11:40 Adams-type spectral sequences (1) "A bridge from (co)homology to homotopy" (Nakai)
      • 11:45-13:00 Adams-type spectral sequences (2) "Solved problems and unsolved problems" (Nakai)
  • Participants:
    • Students 47, others 34, total 81.
    • Affliations of students: Hokkaido University 2, Tohoku University 1, The University of Tokyo 15, Tokyo Metropolitan University 2, Keio University 1, Seikei University 1, Shibaura Institute of Technology 1, Shinshu University 12, Nagoya University 5, Kyoto University 3, Osaka City University 1, Kochi University 2, Kyushu University 1.
    • Undergraduates 17 (sophomore 2, junior 2, senior 13), graduates 30 (M1 10, M2 9, D1 2, D2 3, D3 6), total 47.
This meeting was partially supported by a grant provided by the dean of faculty of science, Shinshu University.