MAU33301 Topics in combinatorial algebraic geometry
| Module Code | MAU33301 |
|---|---|
| Module Title | Topics in combinatorial algebraic geometry |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Marvin Anas Hahn |
| Module Prerequisites | MAU11100 Linear algebra and
MAU22101 Group theory |
Assessment Details
- This is a seminar-style module. Active participation is expected.
- The module consists of weekly talks given by students, weekly assignments and a written 15-20 page report.
- The talk will contribute 40%, the assignments will contribute 20% and the written report will contribute 40% to the final grade.
- The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
- A fail in the continuous assessment will be reassessed by one or more summer assignments in advance of the supplemental session.
Contact Hours
11 weeks of teaching with one seminar per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Move between various equivalent definitions of matroids
- Distinguish between realisable and non-realisable matroids
- Associate matroids to linear algebra data and to combinatorial graphs
- Identify various combinatorial properties of matroids
- Apply various theorem on matroids to combinatorial questions
Module Content
- Basic concepts of matroids
- Equivalent definitions of matroids
- Geometric representations of matroids
- Duality of matroids
- Graphic and transversal matroids
- Minors
- The Scum theorem
- Connectivity in matroids
- Representability of matroids
- Whitney’s 2-isomorphism theorem
- Characteristic polynomials
- Hard Lefschetz theorem for matroids
Recommended Reading
- Matroid theory by Oxley, J. G., Oxford University Press, USA. Chicago (2006)