Below you find the necessary information to get involved in the activities of the Chair of algebraic geometry. The topics are:
If you would like to do a bachelors/masters project or if you would write your masters thesis under the supervision of any of the members of the Chair of Algebraic Geometry, you should contact Zsolt Patakfalvi in e-mail as soon as possible. It is important that you took at least the courses in the algebraic geometry sequence listed below. There are projects available of all difficulties. Some examples:
Bachelors projects: there are multiple options, for example:
- reading about a commutative algebra topic, possibly checking new examples, working out proofs that cannot be found in the literature,
- reading about algebraic geometry topics that are not well presented in the curriculum, for example reading about the more complex analytic part of algebraic geometry, assuming that you took the necessary courses.
- checking questions with a computer.
Masters projects & thesis: algebraic geometry is a subject which is hard to do on a small scale, that is, by just taking a little peep into this area of mathematics. In particular, if you would like to do the master thesis under our guidance, the ideal is to do both the master project and the master thesis with us. Both the masters project and the masters thesis are combinations of the following parts, where the weights of the different parts is tailored to the needs of the actual project:
- studying the parts of the book “Hartshorne: Algebraic Geometry” that was not covered by the course Modern algebraic geometry; this is particularly suggested if you plan to do a PhD in algebraic geometry, as this way you can start your PhD with a solid background,
- reading about applications of the general theory of algebraic geometry, to curves, surfaces, etc.,
- reading about a particular topic,
- thinking about a particular question, possibly coming up with new results, checking new examples, working out proofs that cannot be found in the literature, and
- there is also a possibility to involve computer based checking of examples, or writing code for other reasons.
The topics of masters theses can vary significantly. The main focus of the group is theoretical algebraic geometry in general, but we are happy to host masters theses on related topics such as: commutative algebra, algebraic geometry based cryptography, arithmetic geometry, complex differential geometry, etc.
There is an algebraic geometry sequence of courses hosted jointly with the Chair of Arithmetic Geometry. It is essential that you take these courses if you would like to get involved with us. These courses are also part of the Algebra and Geometry track, so they are not exclusive for algebraic geometry. Many of them are also suggested if you want to learn topology, number theory, group theory, etc. In chronological order the list is:
- BA 5: Rings and modules
- BA 6: Algebraic curves
- MA 1: Modern algebraic geometry
- (future MA 1: Commutative algebra)
- MA 2: Topics in algebraic geometry
We suggest you complement the above sequence with as many courses as possible in algebra, geometry, topology, number theory, differential geometry and complex analysis. But, the members of the Chair of Algebraic Geometry have also used during their research topics such as partial differential equations, measure theory, probability theory, functional analysis.
For a specific list of complementary courses we refer to the list on the homepage of the Algebra and Geometry track. In fact, if you would like to do a PhD in algebraic geometry it is important that you take almost all of the courses there. Note that not all courses listed on the homepage of the Algebra and Geometry track, is given each year.
You can find the list of seminars here. Note that to participate in the non-public seminars of the Chair of Algebraic Geometry you have to contact Zsolt Patakfalvi. Participation is strongly encouraged if you plan to do a PhD in algebraic geometry. Even if you do not understand a single word, just sitting at the seminars and listening to the words and the way people think is an indispensable part of becoming a researcher in algebraic geometry.
On the above link you can already find the online seminar ZAG. If you look at the recorded videos of this and other similar seminars, you can stop them when you hear something that you have never heard abut, and you can look it up over the internet. You can also skip the very technical parts of these talks. This is a very effective way of acquiring an understanding in general the landscape of algebraic geometry. It is highly recommended if you want to do a PhD in algebraic geometry. Some seminars of this type are (the recorded lectures are usually at the bottom of the pages):
- ZAG (general algebraic geometry)
- MAGIC (arithmetic geometry)
- VaNTAGe (arithmetic geometry & number theory)
In case of specific questions about courses suggested, please e-mail Zsolt Patakfalvi or visit him in his office.