# Upcoming Talks

The seminar will meet at 4:30 on Monday in 2-131 unless otherwise noted.

• Nov 202017

### Doug Ravenel (University of Rochester)

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#### Two equivariant approaches to the telescope conjecture

Reporting on joint work with Zhouli Xu and 4 others, I will talk about how equivariant techniques MIGHT be used to settle the telescope conjecture at the prime $2$.

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• Nov 272017

### Kathryn Mann (Brown University)

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#### New progress on spaces of foliated bundles and nonlinear character varieties

A flat $M$-bundle is a topological (or smooth) $M$-bundle with a foliation transverse to the fibers; these are classified by the classifying spaces for $\Homeo(M)$ or $\Diff(M)$ with the discrete topology. In this talk, I will describe an alternative approach to their study, introducing nonlinear analogs of character varieties for representations of discrete groups to groups of homeomorphisms or diffeomorphisms. Our motivation comes from the case of $M=S^1$, where character spaces have a natural interpretation through dynamical invariants of group actions.

In new joint work with M. Wolff, we use this perspective to characterize the isolated points of the character space for representations of surface groups into $\Homeo(S^1)$. Remarkably, these points are precisely the geometric representations, coming from an embedding of the group into a lattice in a Lie subgroup of $\Homeo(S^1)$. This gives a new instance of the classical dynamical theme of rigidity of lattice actions, and progress towards an $h$-principle for transversely projective codimension $1$ foliations.

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• Dec 042017

• Dec 112017

### Julie Bergner (University of Virginia)

The mailing list for this seminar is the MIT topology google group.
Email Mike Hopkins if you want to join the list.