Topics in Geometry (GeoTopics)
Provider: Faculty of Science

Activity no.: 7001-20-07-34 
Enrollment deadline: 16/11/2020
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time16.11.2020, at: 08:00 - 29.01.2021, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserNiels Martin Møller    E-mail address: nmoller@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 2
Scheme groupC
Exam formOral examination
Exam formCourse participation
Exam detailsWe will occasionally give exercises in class, recitations/exercise sessions will focus on the basic background material.
Course workload
Course workload categoryHours
Lectures28.00
Exercises14.00
Preparation114.00
Exam50.00
Sum206.00
Content
Singularities in mean curvature flow: The mean curvature flow of a closed manifold always meets singularities within finite time. The study of such singularities is under intense scrutiny by researchers in geometry. This advanced course aims to bring the participants up to speed with both many now classical aspects as well as the very latest research in this field, via going through original research papers. As needed, we will cover some of the prerequisite advanced material from geometry, partial differential equations and geometric measure theory as we go along.

Learning outcome
Knowledge:
To display knowledge of the course topics and content, at the level of a beginning researcher.

Skills:
To be able to use the acquired knowledge to perform state of the art analysis of the singularities of curvature flows.

Competencies:
To be able to produce independent proofs in extension of the acquired knowledge.

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).

Teaching and learning methods
4 hours of lectures/week + 2 hours of exercises per week for 7 weeks.