Workshop on Unstable Homotopy Theory

Burklund, Robert and Barkan, Shaul and Zhang, Adela and Blom, Thomas and Heuts, Gijs and Horel, Geoffroy and Kuijper, Josefien and Arone, Gregory and Dong, Xiaowen and Konovalov, Nikolai and Balderrama, William and Bachmann, Tom and Behrens, Mark (2024) Workshop on Unstable Homotopy Theory. In: Workshop on Unstable Homotopy Theory. (Unpublished)

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[thumbnail of Robert Burklund, talk 1: Perfect $\mathbb{F}_p$-algebras in homotopy theory] Video (Robert Burklund, talk 1: Perfect $\mathbb{F}_p$-algebras in homotopy theory)
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[thumbnail of Robert Burklund, talk 2: Perfect $\mathbb{F}_p$-algebras in homotopy theory] Video (Robert Burklund, talk 2: Perfect $\mathbb{F}_p$-algebras in homotopy theory)
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[thumbnail of Robert Burklund, talk 3: Perfect $\mathbb{F}_p$-algebras in homotopy theory] Video (Robert Burklund, talk 3: Perfect $\mathbb{F}_p$-algebras in homotopy theory)
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[thumbnail of Shaul Barkan, A chromatic Whitehead theorem] Video (Shaul Barkan, A chromatic Whitehead theorem)
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[thumbnail of Adela Zhang, Universal differentials in the bar spectral sequence] Video (Adela Zhang, Universal differentials in the bar spectral sequence)
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[thumbnail of Thomas Blom, On the chain rule in Goodwillie calculus] Video (Thomas Blom, On the chain rule in Goodwillie calculus)
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[thumbnail of Gijs Heuts, talk 1: Hopf algebras and periodic localizations of homotopy theory] Video (Gijs Heuts, talk 1: Hopf algebras and periodic localizations of homotopy theory)
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[thumbnail of Gijs Heuts, talk 2: Hopf algebras and periodic localizations of homotopy theory] Video (Gijs Heuts, talk 2: Hopf algebras and periodic localizations of homotopy theory)
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[thumbnail of Gijs Heuts, talk 3: Hopf algebras and periodic localizations of homotopy theory] Video (Gijs Heuts, talk 3: Hopf algebras and periodic localizations of homotopy theory)
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[thumbnail of Geoffroy Horel, $E_2$ formality via obstruction theory] Video (Geoffroy Horel, $E_2$ formality via obstruction theory)
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[thumbnail of Josefien Kuijper, The Dehn invariant and spherical scissors congruence as spectral Hopf algebra] Video (Josefien Kuijper, The Dehn invariant and spherical scissors congruence as spectral Hopf algebra)
talk_vidiu_202411121359-01.09.23.770-02.03.48.201-Kuijper_The_Dehn_invariant_and_spherical_scissors_congruence_as_spectral_Hopf_algebra.mp4 - Presentation
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[thumbnail of Gregory Arone, Polynomial functors from groups to spectra] Video (Gregory Arone, Polynomial functors from groups to spectra)
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[thumbnail of Xiaowen Dong, Motivic Toda brackets] Video (Xiaowen Dong, Motivic Toda brackets)
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[thumbnail of Nikolai Konovalov, Algebraic Goodwillie spectral sequence] Video (Nikolai Konovalov, Algebraic Goodwillie spectral sequence)
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[thumbnail of William Balderrama, Unstable synthetic deformations] Video (William Balderrama, Unstable synthetic deformations)
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[thumbnail of Tom Bachmann, $E_{\infty}$-coalgebras and $p$-adic homotopy theory] Video (Tom Bachmann, $E_{\infty}$-coalgebras and $p$-adic homotopy theory)
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[thumbnail of Mark Behrens, Computing unstable stems using the Goodwillie spectral sequence] Video (Mark Behrens, Computing unstable stems using the Goodwillie spectral sequence)
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Abstract

Unstable homotopy theory is about understanding the detailed structure and properties of topological spaces and morphisms between them. Central to this study is the concept of homotopy types (also known as $\infty$-groupoids, animas, or spaces), which classify topological spaces up to weak homotopy equivalence. This subject is rich in both computational and structural aspects: On the one hand, it has been a long-term project to compute algebraic invariant of homotopy types, such as homotopy groups and homology groups of a given topological space. On the other hand, it encompasses the ongoing search for algebraic structures within homotopy types.

Recently there have been many fruitful results in understanding homotopy types by using algebraic and higher categorical techniques. Examples include extension of Quillen's Lie algebra model of rational homotopy types to higher $v_n$-periodic homotopy types, variants and generalizations of Mandell's results on models of finite type p-complete nilpotent CW-complexes, and significant progress in unstable motivic homotopy theory based on the theory of unstable localisation developed by Bousfield and Farjoun.

With these latest advances one can study homotopy types from an algebraic point of view by using tools from the theory of operadic calculus, Koszul duality, Goodwillie calculus, higher category theory and higher algebra. We hope to gather experts and early-career mathematicians working in unstable homotopy theory and adjacent fields at our workshop, to communicate these important results, to promote the exchange of ideas and to stimulate future research in this area.

Item Type: Conference or Workshop Item (Lecture)
Subjects: 3 Geometry and topology > 55-XX Algebraic topology
Depositing User: This Admin
Date Deposited: 29 Nov 2024 13:29
Last Modified: 29 Nov 2024 13:29
URI: https://archive.mpim-bonn.mpg.de/id/eprint/5142

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