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
- Work with the ring of symmetric functions
- Idenfity many different natural bases of this ring
- Relate the theory of symmetric functions to the representation theory of the symmetric group
- Relate different bases via deformations
Module Content
- Partitions
- The ring of symmetric functions
- Bases of the ring of symmetric functions
- Characters of the symmetric group
- The Littlewood-Richardson Rule
- The Hall algebra nd Hall polynomials
Recommended Reading
- Macdonald, I. G. Symmetric Functions and Hall Polynomials. 2nd ed., Oxford University Press, 1995.