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.

Alessio Moscariello , PhD Commutative Algebra, Additive Combinatorics, Semigroup rings, Singularities in positive characteristic, Fewnomials

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)

Kaiwen Zhao, Guest researcher Additive Combinatorics (from Nanning Normal University, China)

Qinghai Zhong, Research Associate Additive Combinatorics and Combinatorial Factorization Theory

Researchers

Former Members