In general the courses suggested for those who would like to participate in the activities of the Chair of Algebraic Geometry are:
- As many bachelors courses as possible in algebra, geometry, topology, number theory, differential geometry and complex analysis. We might be able to use also some partial differential equations background too through the complex differential geometry connections.
- On the masters level primarily: algebraic geometry. Secondarily: any masters courses in the above fields.
More specific list of courses is below. The two courses without which we cannot do anything are set in italics. However, also the other “strongly suggested” ones, and some (your choice which) of the “other suggestions” are required if you want to do a PhD in algebraic geometry at EPFL or elsewhere.
- For doing a Bachelors semester project with us:
- all the second year algebra and topology courses, including the optional Topologie (BA 4) and
- Rings and modules (BA5), Introduction to Algebraic Geometry (MA2 usually, but suggested to be taken in BA6 if you want to do a PhD in algebraic geometry, parallelly with the Bachelors project)
- Also strongly suggested: Introduction to differential manifolds (manifolds = variétés in french!, BA 5-6), Lie algebras (BA 5-6), Galois theory (BA 5-6), Representation theory of finte groups (BA 5-6), algebraic number theory (BA 5-6), Algebraic topology (BA 5-6)
- Possible other suggestions (if time permits): Ordinary differential equations (BA5), Functional analysis I (BA 5-6), Measure theory and integration (BA 5-6), Introduction to partial differential equations (BA 5-6), Analytic number theory (BA 5-6)
- For doing a Masters project with us:
- Everything listed above for the Bachelors semester project, including all the “strongly suggested” courses, but only as many “other suggestions” as time permits (if you did your Bachelors at EPFL), or the equivalent if you did your bahcelors elsewhere.
- Further strongly suggested courses: Introduction to riemannian geometry (MA1-2), Lie groups (if given, MA 1-2), Riemann surfaces (if given: MA 1-2)
- Possible other suggestions: L-functions and random matrices (MA 1-2), Advanced analysis I & 2 (MA 1-2), Functional Analysis II (MA 1-2), Elliptic PDE’s (MA 1-2)
- Doing a Masters thesis with us:
- All the above, except that it is OK to make a selection out of the “other suggestions” category, such that the Introduction to Algebraic Geometry is taken in BA6. Then, it is important that you do your masters project with us, and during this masters project you learn the language of schemes. This project can be unofficially extended for 2 semesters as the topic is very hard. We are open to that in all cases. It is also possible to start working towards the thesis in this unofficial 2nd semester of the masters project, thus gaining more time to obtain some result.
- Getting accepted as a PhD student:
- All the above, optimally including all the “strongly suggested” ones and a nice selection of the “other suggestions”, plus writing an interesting masters thesis.
In case of specific questions about courses suggested, please visit Zsolt Patakfalvi in his office.