For my research I want to somehow
generalize well known results about the Proj of a graded ring to
arbitrary gradings by finitely generated abelian groups. This leads to
the notion of multihomogeneous spectra, first introduced by
Brenner/Schröer in 2007.
It turns out that the grading has major influence on the constructed spectra, in particular on the separatedness.
My final goal is to find a correspondence of the multigrading of a polynomial ring and the separatedness of the corresponding toric prevariety.
I prepare(d) the exercise classes for the following lectures
|Winter Term 2019/2020||Algebraic Geometry I|
|Summer Term 2020||Algebraic Geometry II|
|Winter Term 2020/2021||Algebraic Geometry III|
Linear Algebra I
|Summer Term 2021||Linear Algebra II|
|Winter Term 2021/2022||Algebra|
|Summer Term 2022||Commutative Algebra|
My supervisor Prof. Alex Küronya and me are also currently working on a textbook on elementary math (corresponding to the lecture series `Elementarmathematik') that is going to be published by Springer in the course of 2022.
|24.10.2019||Oberseminar Algebra Ulm||Numer field sieve (talk on my master thesis)|
|22.04.2021||DaFraHeiMai/GAUS-Seminar SoSe 2021||The Betti moduli space|
|09.12.2021||GAUS-Seminar – WiSe 2021/22||A crash course on toric varieties|