The expertise of the **Algebra and Number Theory Group** at the Department of Mathematics and Scientific Computing at the University of Graz
covers topics ranging from commutative algebra, (non-)commutative ring theory, representation theory to singularity theory.

We are particularly interested in the following:

- arithmetic of rings and monoids (the monoids we mainly have in mind are monoids of ideals and monoids of modules)
- interactions between their arithmetic and their algebraic structure, their multiplicative ideal theory, and their factorization theory
- topics in additive combinatorics, including zero-sum problems, addition theorems, and polynomial methods
- understanding and explaining geometric phenomena of algebraic varieties in the presence of singularities, using methods from commutative algebra and representation theory
- the interaction between geometric and homological aspects of singularities, in particular, singularity categories
- geometric and combinatorial aspects of representation theory, in particular, cluster structures

We have close links with the research group Algebraic Structures and Geometry of Martin Kalck. We participate in the Graz School of Discrete Mathematics and the Doctoral Academy Graz .

# Researchers

Eleonore Faber, Univ.-Prof.
(Head)
commutative algebra, (noncommutative) algebraic geometry, representation theory, singularity theory, homological algebra, cluster algebras

Aqsa Bashir, PhD Multiplicative ideal theory, factorization theory, zero-sum theory

Charles Beil, PhD

Nikola Bogdanovic, MSc
(PhD student)

Laura Cossu, PhD University of Cagliari, external member of the Graz School of Discrete Mathematics

Özgür Esentepe, PhD
Commutative Algebra, Representation Theory

Alfred Geroldinger, Ao. Univ.-Prof.
Multiplicative ideal theory, factorization theory, additive combinatorics, zero-sum theory

Florian Kainrath, Ass.-Prof.

Zahra Nazemian, PhD
Module theory, Noncommutative algebra and ring theory, Homological algebra and its application in ring theory

Yurii Neretin, PhD

Nebojsa Pavic, PhD
Algebraic geometry, singularities, homological algebra and derived categories

Mara Pompili, Dott. Mag.
(PhD student)

Balint Rago, MSc
(PhD student)

Andreas Reinhart, Priv.-Doz.
Commutative rings, multiplicative ideal theory, factorization theory

Weihao Yan,
Guest researcher
Additive Combinatorics, Factorization Theory
(supported by Hebei Normal University, China)

Doniyor Yazdonov, MSc
(PhD student)

Qinghai Zhong, Research Associate
Additive Combinatorics and Combinatorial Factorization Theory

# Former Members

- Karin Baur
- Dusko Bogdanic
- Lukas Donner
- Yushuang Fan
- Susan El-Deken
- Ana Garcia Elsener
- Felix Gotti
- David J. Grynkiewicz
- Wolfgang Hassler
- Günter Lettl
- Aihua Li
- Jianrong Li
- Junseok Oh
- Vadim Ponomarenko
- Chanwit Prabpayak
- Sávio Ribas
- Wolfgang A. Schmid
- John Schmitt
- Daniel Smertnig
- Irena Swanson
- Salvatore Tringali
- Gülşen Ulucak
- Hanbin Zhang