6 ECTS credits
168 h study time
Offer 1 with catalog number 4013319FNR for all students in the 1st semester at a (F) Master - specialised level.
The precise content will be determined in consultation with interested students, and will depend on their background and interests. Some of the more advanced topics that could be discussed in the course are:
- Algebraic groups
- Sheaf cohomology
- Fourier-Mukai transforms
- Motives
- Deformation theory
- Noncommutative geometry
- Applications to coding theory and cryptography
- ...
Use of own notes which will be posted on Canvas. Possible references for the course:
- Algebraic Geomtery, a First Course (Harris)
- Algebraic Geometry (Hartshorne)
- Lectures on the Theory of Pure Motives (Murre, Nagel, Peters)
- Fourier-Mukai Tranforms in Algebraic Geometry (Huybrechts)
- Deformations of Algebraic Schemes (Sernesi)
- Algebraic Geometry in Coding Theory and Cryptography (Niederreiter, Xing)
1. Student knows and has insight in the fundamental results of algebraic geometry.
2. Student can look up related properties and structures.
3. Student can prove related properties.
4. Student can make connections with related concepts and other theories.
5. Student can think in function of problem.
6. Student can synthesize and interpret results.
7. Student independently can look up and solve exercises.
8. Student can analyze results.
9. Student can consult and understand recent literature.
10. Student can independently compose a correct mathematics text about the solutions of exercises.
11. Student can draw up a text on another theory independently and report orally.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
Precise details regarding the evaluation will be reported to the students on a yearly basis through Canvas. Interested students are encouraged to contact the course titular as soon as possible.
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)