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Syllabus Singularities of Mean Curvature Flow - 80968
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Last update 11-07-2018
HU Credits: 3

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 2nd Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Jake Solomon

Coordinator Email: jake@math.huji.ac.il

Coordinator Office Hours: By appointment.

Teaching Staff:
Prof Jake Solomon

Course/Module description:
Given a submanifold, it is natural to look for an isotopic submanifold with minimal volume. Minimal submanifolds play an important role in fields ranging from the study of soap bubbles to boundary conditions in quantum gravity. Mean curvature flow is an evolution equation for submanifolds that reduces volume as quickly as possible. In good cases, it converges to a volume minimizing submanifold. However, in general, singularities develop that prevent the continuation of the flow. In this this course, we will learn about the classification of singularities.

Course/Module aims:
Classification of singularities in mean curvature flow.

Learning outcomes - On successful completion of this module, students should be able to:
To understand the basic techniques for classifying singularities of mean curvature flow. To prove long term existence in dimension 2 and for convex hypersurfaces.

Attendance requirements(%):
While there is no formal attendance requirement, students are expected to learn the content of lectures, which may not be available from any of the course reading. Moreover, students are expected to be aware of any announcements made in lecture.

Teaching arrangement and method of instruction: Lecture and exercises.

Course/Module Content:
Introduction to mean curvature flow, blow-up arguments, type 1 singularties, type 2 singularities, long term existence for convex hypersurfaces, long term existence for curves in the plane.

Required Reading:
Mategazza, Carlo, “Lecture Notes on Mean Curvature flow”

Additional Reading Material:
Ecker, Klaus, “Regularity Theory for Mean Curvature Flow”
Zhu, Xi-Ping, “Lectures on Mean Curvature Flows”


Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 100 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information:
 
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.
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