Supervision

If you are interested in working on a project under my supervision, please write me an email.
I am also happy to co-supervise a project.
Here is some good advice by Terry Tao on writing (and reading) mathematics.

Types of projects

Bachelor theses / Bachelorarbeiten (expository work, mini research projects, algorithmic projects)

Zulassungsarbeiten (expository work, mini research projects, algorithmic projects, outreach/popularisation)

Master theses / Masterarbeiten (expository work, small research projects, algorithmic projects)

PhD projects / Doktorarbeiten in arithmetic geometry, number theory, algebraic geometry.

Topics

I am happy to supervise projects related in topics to arithmetic geometry, number theory, algebraic geometry.
I am always open for suggestions and wishes of students and try to provide tasks tailored to the interests and knowledge of the student.

A project can start with reading books or a paper, which can lead to expository work, or to discovering one's own problems. This requires reading with an open mind, and asking questions.
Never stop asking questions, there is no shame in not knowing. Sometimes we find the most interesting problems while asking a seemingly stupid question.

Mathematics advances incredibly fast - and all of us only understand a very very small part of it. It may seem daunting to start, as if one is standing on front of a huge mountain range. But you don't have to climb all the peaks at once - just start with a small hill and let your questions and interests guide you.
My goal is to help you along in this process, to help you develop skills that will help you in the real and in the mathematical world.

Possible fields include:    elementary number theory       algorithmic number theory       non-archimedean geometry          elliptic curves       p-adic cohomology       p-adic Hodge theory       resolution of singularities       Galois representations       cohomological descent       syntomic cohomology

Starting points for projects:    p-divisible groups       local fields       Lie algebras       algebraic groups       elliptic curves       modular forms       syntomic cohomology       non-archimedean geometry       p-adic comprison theorems       rigid cohomology       crystalline cohomology

Some concrete suggestions:    overconvergent Hyodo-Kato complex        the monodromy operator on the Tate curve      finiteness of integral p-adic cohomology       cohomological descent for refinable topologies       minimal models for elliptic curves       impossibility theorems for elementary integration       adelic points       the word problem       Deligne's approach to Nagata compactification       Bloch-Ogus cohomology theory       Galois representations arising from p-divisible groups       Fermat's Last Theorem for regular primes       Selmer's example       famous functions in number theory       the problem of Catalan