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College of Liberal Arts and Sciences | Mathematics

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November 5, 2019 | 2:00 p.m. - 3:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Mohammad Kang, Wayne State University

Title: On the cohomology of the Novikov diagonal, the height n Morava stabilizer group, and U(n)

Abstract: We present new computations related to calculating the stable homotopy groups of spheres. For this, we make use of the K(n)-local Adams-Novikov spectral sequence for Smith-Toda V(n-1) and the decomposition of the stable homotopy groups of spheres, due to Bousfield, Wilson, Morava, Miller, Ravenel and others, into 2(p^n-1)-periodic families for a fixed prime p and non-negative integer n. Our computations are aimed at the input for this spectral sequence, which is the cohomology of the height n Morava stablizer group and which, for p > n+1, coincides with the cohomology of a certain differential graded algebra constructed by Ravenel; and in particular, we restrict our attention to, geometrically, a certain diagonal line in this spectral sequence, which we term the 'Novikov diagonal', or algebraically, the cohomology of the height n Morava stabilizer group where the internal degree is divisible by 2(p^n-1). For p>n+1, we outline our work on a conjecture from the 1970s, which states that the cohomology of the Novikov diagonal is isomorphic to the cohomology of U(n), the unitary group of degree n. Specifically, we've reduced this conjecture down to a special case of an open question by Ravenel, which asks about nonzero differentials in the Ravenel-May spectral sequence. Joint with Prof. Andrew Salch.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.