Higher structures in homotopy theory
| Created: | 2018-07-03 11:16 |
|---|---|
| Institution: | Isaac Newton Institute for Mathematical Sciences |
| Editors' group: | Members of "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. |
Media items
This collection contains 97 media items.
Media items
Configuration spaces and Lie algebras away from characteristic zero
58 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
Hermitian K-theory for Waldhausen infinity categories with genuine duality
38 views
Spitzweck, M
Friday 6th July 2018 - 11:30 to 12:30
Collection: Higher structures in homotopy theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Fri 6 Jul 2018
The model-independent theory of (∞,1)-categories (1)
344 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
46 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
Adelic models for Noetherian model categories (joint work with John Greenlees)
27 views
Balchin, S
Tuesday 2nd October 2018 - 14:00 to 15:00
Collection: Higher structures in homotopy theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 3 Oct 2018
Algebraic models for rational equivariant commutative ring spectra
46 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
57 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 Additivity Theorem for cobordism categories, with applications to Hermitian K-theory
16 views
Steimle, W
Tuesday 21st August 2018 - 14:00 to 15:00
Collection: Higher structures in homotopy theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Thu 23 Aug 2018
An introduction to topological coHochschild homology
73 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
18 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
172 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
18 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
29 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
19 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
250 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
265 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
Derived modular envelopes and moduli spaces of bordered Riemann surfaces
19 views
Berger, C
Tuesday 31st July 2018 - 14:00 to 15:00
Collection: Higher structures in homotopy theory
Institution: Isaac Newton Institute for Mathematical Sciences
Created: Wed 1 Aug 2018
Duality and invertibility using finite resolutions - 2
173 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
33 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
22 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