Seminar: Two new ways in which Dickson algebras inform homotopy theory

Thời gian: 10:00 đến 11:00 Ngày 11/12/2023

Địa điểm: Phòng C101, VIASM, 157 phố Chùa Láng, Hà Nội

Lecturer: Prof. Dev Sinha

Abstract:

Part I - The Curtis-Wellington spectral sequence proceeds from the Ext group as unstable modules over the Steenrod algebra of the cohomology of QS^0 and converges to stable homotopy.  Dana Hunter showed that this cohomology is naturally filtered by ``width’’ with subquotients the “odd submodule” of Dickson algebras.  Thus, the E_2 page of the associated width spectral sequence has zero line which are the Steenrod indecomposables of Dickson algebras, as studied by Hu’ng Peterson.  We elaborate these constructions and share directions of inquiry, including odd primary versions, connection with the Lannes-Zarati homomorphism, and with chromatic homotopy theory.
Part II - Margolis homology both governs some behavior of modules over the Steenrod algebra and serves as the E_2 page of the Adams or Atiyah-Hirzebruch spectral sequence.  We share an inductive approach which takes as input the Margolis homology of Dickson algebras and outputs the Margolis homology of symmetric groups.  Preliminary results indicate non-trivial distribution of Morava K-theory of BS_4 across possible degrees.

Mode of participation: hybrid

Join Zoom Meeting
https://zoom.us/j/98263648478?pwd=TEFQcUZMQSt4YTkydDl3ZitodjdrZz09

Meeting ID: 982 6364 8478
Passcode: 2023