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Mincong Zeng: Dual Steenrod algebra, real cobordism and Morava E-theories

Time: Thu 2019-11-21 10.15 - 12.00

Location: Kräftriket, house 6, room 306 (Cramér-rummet)

Participating: Mincong Zeng, Utrecht University

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In chromatic homotopy theory, Morava E-theories with the action of Morava stabilizer groups play a fundamental role. But computing them, especially in height \(> 2\) is difficult, mainly because of the following reasons:

  1.  The group action is complicated and there is no clean formula.
  2. There is no easy geometric models in height \(>2 \).

In this talk, we will investigate the case when \(p = 2\) and the acting group is a cyclic \(2\)-group and attempt to give answers to the above problems for all heights. I will talk about constructing Morava E-theories equivariantly from the real cobordism spectrum, and how these theories are deeply related to dual Steenrod algebra and its generalizations via the equivariant slice filtration of Hill-Hopkins-Ravenel.

This is joint work with Agnes Beaudry, Lennart Meier and Danny Xiaolin Shi.