Higher structures in homotopy theory

Higher structures in homotopy theory's image
Created: 2018-07-03 11:16
Institution: Isaac Newton Institute for Mathematical Sciences
Description: Workshop
2nd July 2018 to 6th July 2018
Organisers:
Stefan Schwede Rheinische Friedrich-Wilhelms-Universität Bonn
Clark Barwick University of Edinburgh
Julie Bergner University of Virginia
Ieke Moerdijk Universiteit Utrecht

Workshop Theme
Homotopy theory has covered a long distance since its origins, the classification of spaces up to homotopy equivalence. Over the years, various kinds of mathematical structures have been investigated from a homotopical perspective, such as equivariant spaces, rings, C^*-algebras, or varieties. Many different approaches of how to formalize what a “homotopy theory” is were proposed, the most prominent ones being the notions of model category and ∞-category.

The relationship between the different ways to formalize a homotopy theory is now well understood; indeed, for comparing different concepts of homotopy theories, one often wants to consider all of them together as another homotopy theory, i.e., a ‘homotopy theory of homotopy theories’. Somewhat surprisingly, most of the concepts organize themselves into a Quillen model category, and the various approaches are Quillen equivalent. After these individual comparison results, Töen was even able to axiomatically characterize a homotopy theory of homotopy theories.

The homotopy theory of homotopy theories is only the first step in a hierarchy of interesting structures, namely the homotopy theoretic approach to higher categories. From this broader perspective, homotopy theories are just (∞, 1)-categories, where the ∞ indatices a structure with higher morphisms of all levels, and the 1 refers to the fact that all 1-morphisms and higher morphisms are weakly invertible. There are now ways to give rigorous meaning to the notion of (∞, n)-categories i.e., where only higher morphisms in level n and above are invertible. Having a rigorous model category of (∞,n)-categories is a cornerstone for the modern approach to topological field theory, thereby unifying categorical considerations with those of homotopy and manifold theory.

This workshop consists of lecture series as well as individual research talks. The introductory series will explain some of the key methods relevant to many parts of the overarching program; they are intended to invite graduate students and postdocs into the field, as well as to strengthen the common ground of the program participants. The individual talks will inform us about recent developments about higher structures in homotopy theory.
 

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Configuration spaces and Lie algebras away from characteristic zero

   49 views

Knudsen, B
Thursday 6th December 2018 - 11:30 to 12:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 10 Dec 2018


The model-independent theory of (∞,1)-categories (1)

   100 views

Riehl, E
Monday 2nd July 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Tue 3 Jul 2018


A Künneth theorem for configuration spaces of products

   44 views

Hess, K
Thursday 5th July 2018 - 16:00 to 17:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 6 Jul 2018


Algebraic models for rational equivariant commutative ring spectra

   40 views

Kedziorek, M
Tuesday 14th August 2018 - 11:30 to 12:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 15 Aug 2018


Ambidexterity in the T(n)-Local Stable Homotopy Theory

   39 views

Yanovski, L
Tuesday 28th August 2018 - 15:30 to 16:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 3 Sep 2018


An introduction to topological coHochschild homology

   47 views

Hess, K
Tuesday 6th November 2018 - 15:30 to 16:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 7 Nov 2018


C_2 equivariant homotopy groups from real motivic homotopy groups

   15 views

Behrens, M
Thursday 16th August 2018 - 09:00 to 10:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 17 Aug 2018


Configuration spaces of points and real Goodwillie-Weiss calculus

   29 views

Willwacher, T
Tuesday 4th December 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 5 Dec 2018


Connectivity and growth in the homology of graph braid groups

   11 views

Knudsen, B
Tuesday 10th July 2018 - 14:00 to 15:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 11 Jul 2018


Contributed talk - Extended evaluation maps from knots to the embedding tower

   24 views

Kosanović, D
Thursday 6th December 2018 - 16:30 to 17:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 14 Dec 2018


Contributed Talk - The low dimensional homology of Coxeter groups

   13 views

Boyd, R
Thursday 6th December 2018 - 15:00 to 15:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Mon 10 Dec 2018


Derived algebraic geometry I

   182 views

Antieau, B
Wednesday 26th September 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 26 Sep 2018


Derived algebraic geometry II

   51 views

Antieau, B
Thursday 27th September 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 28 Sep 2018


Duality and invertibility using finite resolutions - 2

   169 views

Beaudry, A
Tuesday 25th September 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 26 Sep 2018


Dualizability in the higher Morita category

   25 views

Scheimbauer, C
Friday 6th July 2018 - 10:00 to 11:00

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Fri 6 Jul 2018


Embeddings, operads, graph-complexes

   13 views

Turchin, V
Tuesday 4th December 2018 - 14:30 to 15:30

Collection: Higher structures in homotopy theory

Institution: Isaac Newton Institute for Mathematical Sciences

Created: Wed 5 Dec 2018


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