Fall 2020

This semester Juvitop will be about The Coboridsm Hypothesis after Hopkins-Lurie.

We meet at 3:59 on Wednesday in zoom unless otherwise noted.

Discussion sections will be on Tuesdays at 3pm. Times are EST.

• Sep 092020
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Araminta Amabel

Notes:

References:

Videos:

What does the cobordism hypothesis say? Why did anyone ever hypothesize it? This talk is based on pages 2-15 of Lurie's paper. We introduce Atiyah's definition of a topological field theory and examine what data a TFT provides in dimensions 1 and 2. Using these examples, we motivate Baez and Dolan's Cobordism Hypothesis.

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• Sep 152020
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• Sep 162020
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n-Fold Segal Spaces

Speaker's Notes

Videos:

• Introduction to higher categories, dualizability, and applications to topological field theories, Part 1 and Part 2 by C. Scheimbauer

Pages 24-34 of Lurie's paper

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• Sep 222020
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• Sep 232020
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Jackson Van Dyke

Guided by what we know about finite-dimensional vector spaces, we will first define the notion of a dualizable object in any monoidal category. Then, guided by what we know about adjoint functors, we will define a notion of duality for 1-morphisms in any 2-category. With these two definitions in hand, we will define what it means for an object of a monoidal (∞,n)-category to be k-dualizable.

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• Sep 292020
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• Sep 302020
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Kiran Luecke

Pages 43-48 of Lurie's paper

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• Oct 062020
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• Oct 072020
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Ishan Levy

Page 51 of Lurie's paper

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• Oct 132020
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TBD

Pages 52-57 of Lurie's paper

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• Oct 142020
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Lucy Yang

Pages 57-61 of Lurie's paper

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• Oct 212020
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Micah Darrell

Pages 61-70 of Lurie's paper

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• Oct 282020
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Cameron Krulewski

Pages 70-79 of Lurie's paper

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• Nov 042020
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Dylan Wilson

Pages 79-86 of Lurie's paper

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• Nov 112020
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Tashi Walde

References:

Videos:

Recall the definition of E_n-algebras and define topological chiral homology. Describe the class of TFTs that can be produced using topological chiral homology. Formulate a version of the cobordism hypothesis in terms of topological chiral homology (Theorem 4.1.24).

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• Nov 182020
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Cobordism Hypothesis in Low Dimensions

References:

"Discuss some consequences of the cobordism hypothesis and related results in the case of manifolds of dimension 1 and 2. [...] Relate the contents of this paper to the work of Costello and to the Chas-Sullivan theory of string topology operations on the homology of loop spaces of manifolds"

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• Nov 252020
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Will Stewart

"Describe a generalization of the cobordism hypothesis, which gives a geometric description of symmetric monoidal (∞, n)-categories (again assumed to have duals) having more complicated presentations."

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• Dec 022020
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Morgan Opie

Use the material from the previous talk "to sketch a proof of a version of the Baez-Dolan tangle hypothesis, which characterizes (∞, n)-categories of embedded bordisms and can be regarded as an “unstable” version of the cobordism hypothesis."

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This seminar is organized by Araminta Amabel, Peter Haine, and Lucy Yang.