NMAK21002U Cancelled Topics in Geometry
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
We will generally be concerned with various advanced topics from
modern and classical differential geometry, geometric analysis,
Riemannian geometry and topology - close to active areas of
research - such as: Minimal surfaces, prescribed curvature
problems, variational problems in geometry, curvature flows,
geometric analytical methods, with the precise contents varying
each year and depending on the interests of the participants.
Fall 2023: A tentative plan for this year
is to give an introduction to the modern theory of minimal
2-surfaces in 3-manifolds, via excerpts from
Colding-Minicozzi's book A Course in Minimal Surfaces
(AMS, 2011) plus other relevant notes/articles. Time permitting we
will also include some applications to other areas of geometry and
topology.
Contents in past years:
Fall 2021: Themed "Interactions
Between Topology & Geometric Analysis", the main
topics we covered were:
(1) Proof of Hopf's Theorem on uniqueness of the round sphere
as the only genus 0 constant mean curvature 2-dimensional closed
surface in R3, i.e.
"(sometimes) soap bubbles are round" (via the
Poincaré-Hopf index of vector fields combined with complex
analysis, among other things).
(2) Proof of existence of non-trivial closed geodesic curves on any
smooth closed n-dimensional manifold, via so-called min-max
variational methods, which make use of some basic algebraic
topology (homotopy groups) combined with L2-theory for
differential (Euler-Lagrange) equations.
Fall 2020: This year, the course ran
informally, and we discussed advanced topics in Mean Curvature
Flow, such as gluing problems and uniqueness questions for
singularity models in the flow.
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Academic qualifications equivalent to a BSc degree is recommended.
Please note that to prepare lectures as a participant in this topics course is a substantial time commitment. So participants should plan their time accordingly.
- Category
- Hours
- Lectures
- 36
- Preparation
- 143
- Theory exercises
- 27
- Total
- 206
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment
- Type of assessment details
- Weekly written assignments (7 such in total) combined with two
in-class oral presentations:
- One lecture (45 minutes) about a relevant topic (to be decided together with the lecturer or teaching assistant).
- One short presentation of a homework solution (to be decided together with the lecturer or teaching assistant).
The written assignments together are weighted 50%, the in-class oral presentations together are weighted 50%, and the course performance is assessed as a whole. - Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
30 minutes oral exam without preparation time and without aids.
Criteria for exam assesment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Course information
- Language
- English
- Course code
- NMAK21002U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 1
- Schedule
- A
- Course capacity
- No limit
The number of seats may be reduced in the late registration period
Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Niels Martin Møller (NMoller@math.ku.dk)