Department of Mathematical Sciences > Research > Algebra and Number Theory > Guidance for students

General information: For bachelor projects: Have a look at the bachelor catalog.

You can get a good idea of what kinds of projects are possible in algebra and number theory by having a look at previous projects.

You are always welcome to contact any of us if you have ideas for projects or reading courses.

Specialized information:

Non commutative ringtheory and non commutative algebraic geometry (Søren Jøndrup)
Number Theory (Ian Kiming, Morten Risager, Christian U. Jensen)

Non commutative ringtheory and non commutative algebraic geometry (Søren Jøndrup):

Students wishing to specialize in non commutative algebra  should have taken the courses Algebra 3 and modern algebra (or commutative algebra). Some knowledge of homological algebra is also necessary for some of the many different projects in commutative and non commutative ringtheory.

Among the possible projects  for master thesis are:

i) From structure of projective modules to stable range.
ii) PI algebras and their identities.
iii)Non commutative localization and quotient rings.
iv) Homology for non commutative curves.
v) Non commutative factorization.
vi)Quadratic algebras and point modules.

Number theory (Ian Kiming):

Bachelor projects: Have a look at the bachelor catalog

Master's students: Students wishing to specialize in number theory (Ian Kiming) should
take the courses Algebra 3 and either Algebraic Number Theory or
Elliptic Curves.

It is also an excellent idea to take one or both of the courses
Homological Algebra and Algebraic Geometry.

Many different projects/theses in number theory are possible:
Classical topics in algebraic number theory, more modern topics in
elliptic curves, modular forms, Galois representations, and also
various topics related to cryptography (factorization and primality
testing).

Specializing in number theory is also possible under the guidance of
Morten Risager or Christian U. Jensen.