Higher structures in homotopy theory: Recent Episodes

Cambridge University

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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Richter, B Tuesday 18th December 2018 - 15:30 to 16:30

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Botvinnik, B Tuesday 18th December 2018 - 14:00 to 15:00

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

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Henriques, A Friday 7th December 2018 - 10:00 to 11:00

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Nariman, S Friday 7th December 2018 - 11:30 to 12:30

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Budney, R Friday 7th December 2018 - 13:30 to 14:30

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Crowley, D Friday 7th December 2018 - 14:30 to 15:30

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

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Berglund, A Thursday 6th December 2018 - 09:00 to 10:00

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

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Hebestreit, F Wednesday 5th December 2018 - 11:30 to 12:30

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Vespa, C Wednesday 5th December 2018 - 10:00 to 11:00

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Malkiewich, C Wednesday 5th December 2018 - 09:00 to 10:00

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

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Wahl, N Tuesday 4th December 2018 - 16:00 to 17:00

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

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Lueck, W Tuesday 4th December 2018 - 09:00 to 10:00

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Ravenel, D Friday 30th November 2018 - 14:00 to 15:00

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Ayala, D Tuesday 27th November 2018 - 15:30 to 16:30

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Ravenel, D Thursday 26th November 2018 - 14:00 to 15:00

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Ravenel, D Monday 19th November 2018 - 14:00 to 15:00

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Bohmann, A Tuesday 13th November 2018 - 15:30 to 16:30

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Ravenel, D Monday 12th November 2018 - 14:00 to 15:00

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Ravenel, D Wednesday 17th October 2018 - 14:00 to 15:00

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Ravenel, D Monday 15th October 2018 - 14:00 to 15:00

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

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Broto, C Tuesday 6th November 2018 - 14:00 to 15:00

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Hesselholt, L Tuesday 23rd October 2018 - 15:30 to 16:30

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Oliver, R Tuesday 16th October 2018 - 15:15 to 16:15

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Böhme, B Tuesday 9th October 2018 - 15:30 to 16:30

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Ching, M Tuesday 9th October 2018 - 14:00 to 15:00

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Hesselholt, L Monday 8th October 2018 - 16:00 to 17:00

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Grodal, J Tuesday 2nd October 2018 - 15:30 to 16:30

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Balchin, S Tuesday 2nd October 2018 - 14:00 to 15:00

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Behrens, M Friday 28th September 2018 - 14:30 to 15:30

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Quick, G Friday 28th September 2018 - 11:30 to 12:30

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Xu, Z Friday 28th September 2018 - 10:00 to 11:00

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Heuts, G Thursday 27th September 2018 - 14:30 to 15:30

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

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Wahl, N Tuesday 18th September 2018 - 15:30 to 16:30

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Schlichtkrull, C Tuesday 18th September 2018 - 14:00 to 15:00

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Patchkoria, I Tuesday 11th September 2018 - 15:30 to 16:30

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Bruner, R Tuesday 11th September 2018 - 14:00 to 15:00

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

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Hahn, J Tuesday 25th September 2018 - 14:30 to 15:30

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Naumann, N Tuesday 25th September 2018 - 11:30 to 12:30

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

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Meier, L Monday 24th September 2018 - 16:00 to 17:00

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Beaudry, A Monday 24th September 2018 - 10:00 to 11:00

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Ausoni, C Monday 24th September 2018 - 14:30 to 15:30

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Naumann, N Monday 24th September 2018 - 11:30 to 12:30

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

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Hebestreit, F Tuesday 21st August 2018 - 15:30 to 16:30

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Steimle, W Tuesday 21st August 2018 - 14:00 to 15:00

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Wickelgren, K Friday 17th August 2018 - 11:30 to 12:30

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Yarnall, C Friday 17th August 2018 - 10:00 to 11:00

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Asok, A Friday 17th August 2018 - 09:00 to 10:00

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Morel, F Thursday 16th August 2018 - 16:00 to 17:00

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Bohmann, A Thursday 16th August 2018 - 11:30 to 12:30

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Bachmann, T Thursday 16th August 2018 - 10:00 to 11:00

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Merling, M Thursday 16th August 2018 - 14:30 to 15:30

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

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Ravenel, D Wednesday 15th August 2018 - 09:00 to 10:00

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Gerhardt, T Wednesday 15th August 2018 - 11:30 to 12:30

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Roendigs, O Wednesday 15th August 2018 - 10:00 to 11:00

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

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Stojanoska, V Tuesday 14th August 2018 - 16:00 to 17:00

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Hoyois, M Tuesday 14th August 2018 - 14:30 to 15:30

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Levine, M Tuesday 14th August 2018 - 09:00 to 10:00

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Barwick, C Monday 13th August 2018 - 16:00 to 17:00

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Dugger, D Monday 13th August 2018 - 10:00 to 11:00

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Land, M Friday 10th August 2018 - 14:00 to 15:00

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Arone, G Tuesday 31st July 2018 - 15:30 to 16:30

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Berger, C Tuesday 31st July 2018 - 14:00 to 15:00

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Barwick, C Tuesday 24th July 2018 - 15:30 to 16:30

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Schick, T Tuesday 24th July 2018 - 14:00 to 15:00

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Dundas, B Tuesday 17th July 2018 - 15:30 to 16:30

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Bergner, J Tuesday 17th July 2018 - 14:00 to 15:00

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

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Spitzweck, M Friday 6th July 2018 - 11:30 to 12:30

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

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

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Nikolaus, T Thursday 5th July 2018 - 11:30 to 12:30

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Haugseng, R Thursday 5th July 2018 - 13:30 to 14:30

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Riehl, E Thursday 5th July 2018 - 10:00 to 11:00

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Nikolaus, T Wednesday 4th July 2018 - 11:30 to 12:30

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Riehl, E Wednesday 4th July 2018 - 10:00 to 11:00

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Francis, J Tuesday 3rd July 2018 - 14:30 to 15:30

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Nikolaus, T Tuesday 3rd July 2018 - 11:30 to 12:30

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Dyckerhoff, T Tuesday 3rd July 2018 - 13:30 to 14:30

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Riehl, E Tuesday 3rd July 2018 - 10:00 to 11:00

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Yeakel, S Monday 2nd July 2018 - 16:00 to 17:00

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Francis, J Monday 2nd July 2018 - 14:30 to 15:30

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Dyckerhoff, T Monday 2nd July 2018 - 13:30 to 14:30

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Nikolaus, T Monday 2nd July 2018 - 11:30 to 12:30

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