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Thomas Blom: Cooking up model structures on ind- and pro-categories

Tid: On 2021-11-10 kl 16.00 - 18.00

Plats: Kräftriket, House 5, Auditorium 14 and Zoom: 692 9140 5686

Licentiand: Thomas Blom

Granskare: Clark Barwick (University of Edinburgh)

Huvudhandledare: Gregory Arone

Abstract

The overarching theme of the three papers in this licentiate thesis is the construction of Quillen model structures on ind- and pro-categories.

In the first paper, a general method for constructing model structures on ind- and pro-categories is described. This method can be be used to construct "profinite" analogues of many known model structures, but it can also be applied to some interesting other cases. It recovers model structures that were already known to exist while it also produces several new and interesting model structures.

The second paper describes a way of constructing a model category of "profinite" infinity-operads and studies some basic properties of this model category. This construction is similar in spirit to that of the first paper, but there are some subtle differences that make it more involved.

In the third paper, the general method of the first paper is used to construct a model category of noncommutative CW-complexes. This model category is then used to obtain a streamlined proof of a result by Arone, Barnea and Schlank, which states that the category of noncommutative CW-spectra is Quillen equivalent to the category of spectral presheaf on a certain category of finite-dimensional matrix algebras.

Read the thesis on DiVA