Time: 2:00 - 6:00 PM
Location: AUC Tahrir Campus
Building and Classroom: Hill House 406
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Algebraic geometry is a branch of mathematics that studies algebraic varieties. A typical question would be to classify all curves in the plane which are the solution sets of equations like P(x,y)=0 where P(x,y) is a polynomial in two variables, up to a certain notion of equivalence.
Being a very old subject, many tools have been developed over the years in order to answer some of those questions (and to introduce new ones). Sheaves and sheaf cohomology have been brought into algebraic geometry by Cartan and Serre, who created a new language that is extremely useful in the study of algebraic geometry. We shall follow a hybrid approach, focusing on the geometry of complex projective varieties.
As of today, it is clear that algebraic geometry is a beautiful and a useful subject, that has applications in many areas of science such as Mathematical Physics and Computer Science. The goal of this workshop would be to survey some of the methods of the algebraic geometry.
Simon Donaldson - Riemann Surfaces
Hartshorne - Algebraic Geometry
We will assume a good command of general topology and abstract algebra. The latter includes abstract linear algebra (i.e. quotients of vector spaces, isomorphism theorems etc...) and elementary ring and field theory (i.e. ideals, quotients, the isomorphism theorems, etc...).
We will also some basic assume knowledge of the notion of analytic/holomorphic functions.
Some References for the Prerequisites.
This is a good source to review linear algebra is the following set of notes.
Link: https://people.math.ethz.ch/~kowalski/script-la.pdf
For point set topology, a good set of notes are:
Link : https://www.topologywithouttears.net/
For abstract algebra, we recommend Artin's "Abstract Algebra" - Second Edition.
The definition of an analytic function in several variables is on the first page of this document:
Link: https://webspace.science.uu.nl/~looij101/kahler.pdf
Extra. Even though we will review the notion of tensor products of vector spaces, we recommend that the participants familiarize themselves with this notion. The last chapter of the linear algebra notes linked above, contains all we need.
This will be an intense mathematical learning experience. We will have two lectures and two exercise sessions daily for an entire week. During the exercise sessions, the students will work together (with our help) to solve problems about the content of the lectures. The exercises make up a crucial part of the workshop and it is the only way to absorb the material in time for the next topic.
The goal is to guide you in exploring this beautiful area of mathematics while forming long lasting mathematical connections with your peers. We hope you will join us and have a great deal of fun ;)
Important: At least one day may be held online (details TBA)
Exercises can be found here
Registration for this workshop closed at noon on the 27th of July.
Please note that Emails will be sent to you on the Email address you provide us with on the form, so make sure you have easy access to it and check your spam folder regularly for updates sent to you by our organizing committee.