Faculty of Science

Mean Curvature Flow: Recent Progress on Singularity Analysis and Applications
Provider: Faculty of Science

Activity no.: 5569-24-07-31
	Enrollment deadline: 24/04/2024

Place

Department of Mathematical Sciences

Date and time

29.04.2024, at: 09:00 - 03.05.2024, at: 16:00

Regular seats

ECTS credits

2.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Niels Martin Møller E-mail address: nmoller@math.ku.dk

Written language

English

Teaching language

English

Exam form

Course participation

Exam details

Information will follow

Course workload

Course workload category	Hours
Preparation	39.00
Lectures	30.00

Sum	69.00

Content

There has been recent progress on singularity analysis and subsequent applications of the mean curvature flow, by several groups of researchers, in problems involving the generic mean curvature flow and relatedly the low entropy Schoenflies problem.

The goal of the course is to give a substantial overview of these very recent, important results and the techniques involved directly from the experts that developed them.

Formal requirements

Masters with courses in geometry and PDE, as well as some exposure to minimal surfaces and geometric flows.

Learning outcome

Knowledge:
- Learn about the different approaches to the generic mean curvature flow by Schulze, Sun (and their collaborators)
- Learn about the low entropy schoenflies conjecture and the approaches to it by Bernstein, Schulze (and their collaborators)

Skills:
- Learn about some of the most important technical ingredients that go into the lecturers work.

Competences:
- To be able to apply the author’s techniques in their own work, if the occasion ever arises.

Target group

Fairly advanced grad students and postdocs in geometric analysis.

Teaching and learning methods

2 hour lectures by each lecturer per day of the masterclass week, with ample time for the participants to discuss with the lecturers and amongst themselves.

Lecturers

Jacob Bernstein, Johns Hopkins University
Ao Sun, Lehigh University
Felix Schulze, University of Warwick

Jacob Bernstein (JHU) and Felix Schulze (Warwick) are renowned senior mathematicians, with publications in many of the world’s top journals.
Ao Sun (Lehigh) is a younger but rising force in the field of geometric analysis.
Felix, with his collaborators (and based on estimates proven by Niels M. Møller et al.), has recently made very strong progress on generic mean curvature flow in dimension up to 5.
Ao Sun has also made very strong progress on developing generic mean curvature flow by a different approach.
Schulze and his collaborators used their generic mean curvature flow results to show a “low entropy Schoenflies” result in dimension 4. Bernstein and his collaborator showed this around the same time using the mean curvature flow but by a different technique by making progress on how the topology of the flow may change as one passes through an asymptotically conical singularity.

Remarks

Course coordinators: Alexander Mramor & Niels Martin Møller.

Read more and sign up at the course page: https://www.math.ku.dk/english/calendar/events/mean-curvature-flow-2024/

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