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Infinity Operads and Manifolds
Provider: Faculty of Science

Activity no.: 7001-25-07-31
Enrollment deadline: 15/06/2025
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time11.08.2025, at: 09:00 - 15.08.2025, at: 16:00
Regular seats100
ECTS credits2.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserNathalie Wahl    E-mail address: wahl@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Exam formContinuous assessment
Exam formActive participation during the campus course
Exam detailsAttending the lecture series, active participation in the exercise sessions.
Course workload
Course workload categoryHours
Lectures15.00
Theory exercises20.00
Preparation24.00
Sum59.00
Content
We will cover various advanced topics in modern and classic differential geometry and Riemannian geometry, such as prescribed curvature problems, variational problems in geometry, curvature flows, geometric analytical methods, with the precise content depending on the interests of the participants.

Aim and content
The course aims to introduce the participants to infinity operads, which have been at the heart of of many recent developments in homotopy theory.

Haugseng is an expert in infinity-operads and has done much of the foundational work in the area. He will give an elementary introduction to infinity operads as well as application examples in his lecture series.

Scheimbauer is an expert in the interconnected fields of topological field theory, manifolds, and higher categories. She will give a lecture series explaining how infinity operads are used in defining and studying (constructible) factorisation algebras.

Robertson has been pioneering the idea of modular infinity operads, being an author of the foundational book on these. She will give a lecture series explaining this, focusing on the case of surfaces and the relation to the Grothendieck-Teichmüller group.

Formel requirements
Recommended Academic Qualifications: Knowledge of algebraic topology and geometric topology at the level taught in Masters courses. Experience with higher categories or operads is useful, but not required.

Learning outcome
Knowledge:
• The students will gain an understanding of the foundational results on infinity-operads, a concept which appears in various branches of modern algebraic topology.
• The students will acquire a vision for the potential applications of infinity operads and manifolds.

Skills:
• To be able to follow future research talks that make use of infinity operads.
• To be able to apply the theory of infinity operads to new research directions

Competences:
• To be able to produce independent proofs of basic results involving (modular) infinity-operads.
• To be able to discuss current research with experts at an international level

Literature
Selections of original research articles. Supporting lecture notes will be provided for some topics. For other topics, we might use parts of the following examples of literature:
K. Ecker: Regularity theory for mean curvature flow, Birkhäuser 2004.
C. Mantegazza: Lecture notes on mean curvature flow, Birkhäuser 2012 (corrected printing).

Target group
Infinity operads have been foundational to many recent developments in algebraic and geometric topology and because of this have become an essential topic to learn for young researchers in the field. The course is intended for those PhD students and early career researchers who would like to learn about infinity operads and their applications to manifolds.

Teaching and learning methods
The masterclass will consist of three lecture series, introducing infinity operads and their connections to manifolds.
These will be accompanied by exercise sessions and informal discussion sessions in which the participants can practice the tools which are discussed theoretically in the lectures.

Lecturers
Guest Lecturers:
Marcy Robertson, University of Melbourne
Rune Haugseng, NTNU, Trondheim
Claudia Scheimbauer, TU Munich

Remarks
Registration deadline:
For funding: 15th May
Without funding: 15th June

Registration will open in the fall of 2024.

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