Principal Bundles in Derived Differential Geometry

Student: Ajvaz`yan Arshak

Educational Programme: Mathematics (Master)

Year of Graduation: 2025

A site of finite coverings on the category of smooth derived loci is constructed. It is noted that this is the maximal subcanonical site of open coverings on it. It is proved that the associated topos of smooth derived stacks $\Stack$ is local but not locally contractible. As a consequence, it is not cohesive. The constructed setting is of interest in how it handles notions related to infinity and compactness, which play a crucial role in Lie group theory, principal $G$-bundles, and related topics. The long-term goal of the research is to reconstruct differential geometry in this generality, encompassing many classically interesting contexts, with such keywords as manifolds with corners and singularities, orbifolds, Fukaya categories, Gromov–Witten theory, and Batalin–Vilkovisky formalism.

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses