## Spring 2019

This semester Juvitop will be about Moduli Spaces of Manifolds.

We meet at 4:30 on Wednesday in Harvard Science Center 304 unless otherwise noted.

Here is our syllabus for the semester.

• Feb 202019
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### Sander Kupers

Notes taken by Lucy Yang

I will give an overview of the recent program to study manifolds and their diffeomorphisms through moduli spaces. In particular, I will explain the goals of the program, the techniques involved, and the results it obtains for particular classes of manifolds. This talk should be accessible to graduate students with a basic knowledge of differential and algebraic topology.

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• Feb 272019
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### Lucy Yang

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• Mar 062019
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### Robin Elliott

The group completion theorem gives the homology of the group completion of a topological monoid. We'll sketch a proof of the group completion theorem. We'll also set up the theorem in a more general context of topological categories instead of topological monoids.

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• Mar 132019
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### Dexter Chua

I will prove the Barratt–Priddy–Quillen–Segal theorem. From the point of view of this seminar, this theorem provides an explicit description of (the group completion of) the moduli space of compact zero dimensional manifolds. This will serve as a blueprint for the proof of the Galatius–Madsen–Tillman–Weiss theorem about the moduli space of higher dimensional manifolds, which will be discussed in the Talbot workshop.

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• Mar 272019
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### Araminta Gwynne

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• Apr 032019
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### Alexander Kupers

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This seminar is organized by Araminta Gwynne, Morgan Opie, and Lucy Yang.