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Degree theses

Members of the Arithmetic Geometry group

Topics

Potential topics for your bachelor, master or lehramts thesis are in the areas of
Algebraic Geometry, Commutative Algebra or Number theory. More concretely:

Algebraic varieties over finite, local or global fields
L-functions and their special values
Modular forms
Non-archimedean analysis, tropical geometry
Arakelov geometry
Higher cohomological invariants in arithmetic geometry
Motives, motivic homotopy theory and motivic cohomology
Algebraic K-theory
Elliptic curves and abelian varieties
Iwasawa theory
Higher categories, higher topoi
Derived algebraic geometry
Equivariant and chromatic homotopy theory, elliptic cohomology

Past and future courses

Courses suitable for students in the third year or higher:

Lectures

WS 24/25: Algebraic Topology I, 4+2 SWS, Denis-Charles Cisinski
WS 24/25: Diophantine Geometry I, 4+2 SWS, Walter Gubler
WS 24/25: Algebraic Number Theory I, 4+2 SWS, Klaus Künnemann
SS 25: Diophantine Geometry II, 4+2 SWS, Walter Gubler
SS 25: Non-Archimedean Banach Algebras (Algebraic Number Theory II),
4+2 SWS, Klaus Künnemann
SS 25: Algebraic Topology II, 4+2 SWS, Tashi Walde
WS 25/26: Non-Archimedean Analytic Geometry, 4+2 SWS, Klaus Künnemann

These courses will be continued by future lectures and seminars.

Seminars

WS 24/25: The Bloch-Kato Conjecture/Rost-Voevodsky Theorem, Denis-Charles Cisinski, Niklas Kipp
WS 24/25: Seminar: Parametrized semiadditivity, Denis-Charles Cisinski, Bastiaan Cnossen, Sil Linskens, Claudia Scheimbauer
WS 24/25: Seminar: Abelian Varieties, Guido Kings, Julio de Mello Bezerra

How to find an advisor for your bachelor thesis, your master thesis or your admission paper for teacher students (Zulassungsarbeit Lehramt vertieft):

Contact your preferred advisor early on.
If you are planning to write a bachelor thesis with a focus on Arithmetic Geometry, you should attend two of the lectures Algebraic Geometry I+II, Algebraic Number Theory I+II or similar lectures assigned to the modules BV and MArGeom in your fifth and sixth semester. At the end of the lecture period of your fifth semester at the latest, you should look for an advisor for your bachelor thesis and register for their bachelor seminar in your sixth semester. It is also advisable to attend a seminar with the desired advisor in the fifth semester or earlier. The topic of a bachelor thesis often results from a seminar.
In order to write an admission paper for teacher students (Zulassungsarbeit Lehramt vertieft), you should have successfully completed the lectures Algebra and Analysis III and you should complete a seminar with your future advisor. Please contact an advisor of your choice for further details.
For the exact event and time planning for the master's program, please discuss this individually with your preferred advisor during the first year of study.
For the exact event and time planning for the master's program, please discuss this individually with your preferred advisor during the first year of study.

We strongly recommend you to getting to know possible advisors for bachelor and master theses early on in your studies by taking part in relevant seminars.