Juvitop Seminar
Spring 2023
This semester Juvitop will be about Floer Homotopy Theory.
We meet at 3:59 on Wednesday in 2151 unless otherwise noted.

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Natalie Stewart
This talk will be a bird's eye view of the foundations of stable homotopy theory; without delving into models, we will sample some classical homotopy theory in the language of infinity categories. We will define stable infinity categories and t structures, emphasizing the derived category as a guiding example. We will conclude by defining the infinity category of spectra and listing some properties, including its relationship to spaces and the derived category.
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Daniel AlvarezGavela
References:
Review Morse functions, Morse lemma, Morse charts, (pseudo)gradient flows, stable and unstable manifolds. Define the Morse complex/Morse homology. Maybe discuss how the moduli of gradient flows can be compactified to the moduli of broken trajectories as a teaser trailer for next time.
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Cameron Krulewski
References:
Given a finitedimensional, compact Riemannian manifold X and a MorseBott function f from X to R satisfying the Smale transversality condition, we can construct the flow category. From this category, we would like to be able to recover the stable homotopy type of X. I will discuss the structure carried by moduli spaces of gradient flow lines and how this provides the information to recover the suspension spectrum of X. This talk is a warmup for later, when we generalize to the infinitedimensional case.
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 Abouzaid's Floer Homotopy talks at Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory (see also Amanda Hirschi's texed notes)
 BlumbergAbouzaid MSRI lectures 12: talk 1 talk2
Isabel Longbottom
References:
Flow categories, flow modules and their bordisms, quasicategory of flow categories, the quasicategory of flow categories is stable.
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Natalia PachecoTallaj
Describe how the boundary strata of the Morse moduli space give a Maurer Cartan element in a graded spectrum.
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Ishan Levy
Define the moduli stack of broken lines and factorizable spaces over it. Relate the AbouzaidBlumberg and LurieTanaka pictures: an object in AbouzaidBlumberg's category gives a factorizable space over Broken with framing.
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Classical Floer Theory in the Symplectic Setting
Clair Xinle Dai
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No Talk: MIT Spring Break
None
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Sanath Devalapurkar
References:
For spin manifolds with almost complex structure, the Floer homotopy type determined by the smooth, compact flow category defined in CJS is given by the suspension spectrum of the free loop space.
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Complex cobordism, Hamiltonion loops, and global Kuranishi charts
Charlotte KirchhoffLukat
References:
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Floer theory and algebraic Ktheory
Daniel AlvarezGavela
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Zihong Chen
Define Fukaya categories and show they are A_∞.
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Bauer Furuta Invariants
Mary Stelow
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TBD
TBD
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This seminar is organized by Cameron Krulewski, Ishan Levy, Natalia PachecoTallaj, and Mary Stelow.