Spring 2019

In Spring 2019, Juvitop was about Moduli Spaces of Manifolds.

Here is our syllabus for the semester.

• • Feb 202019
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  An introduction to moduli spaces of manifolds

  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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  Characteristic Classes of Manifold Bundles

  Lucy Yang

  References:

  • Monoids of Moduli Spaces of Manifolds Section 2.1
  • Moduli Spaces of Manifolds: A User's Guide Section 2
  • On the geometric nature of characteristic classes of surface bundles for the fun fact

  Notes

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• • Mar 062019
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  Group Completion

  Robin Elliott

  Reference: Stable Homology of Automorphism Groups of Free Groups Lemma 4.17

  Notes

  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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  The Barrat–Priddy–Quillen–Segal Theorem

  Dexter Chua

  Reference: Lectures on Diffeomorphism Groups of Manifolds

  Notes

  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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  Cobordism Categories

  Araminta Amabel
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• • Apr 032019
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  Group Completion for Cobordism Categories

  Alexander Kupers

  Reference: Stable Mapping Class Groups and $Q\mathbb{CP}^{\infty}_+$

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This seminar was organized by Araminta Amabel, Morgan Opie, and Lucy Yang.