# Algebra/Topology seminar

Speaker: Jeremy Hahn (MIT)

Title: Using the Adams spectral sequence to make smooth structures on manifolds

Abstract: I will explain work, joint with Robert Burklund and Andrew Senger, that uses Adams spectral sequence computations at the primes 2 and 3 to produce smooth structures on PL manifolds.  This settles both recent conjectures of Galatius and Randal-Williams as well as questions raised in 1962 by C.T.C. Wall.  Our approach combines modern understanding of E-infinity Thom spectra with Pstragowski's theory of synthetic spectra.  I will indicate how further knowledge of vanishing sectors in the Adams spectral sequence, at both primes 2 and 3, may lead to further results in the classification of highly connected manifolds.