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 .


Eleonore Faber
Eleonore Faber, Univ.-Prof. (Head) commutative algebra, (noncommutative) algebraic geometry, representation theory, singularity theory, homological algebra, cluster algebras
Aqsa Bashir
Aqsa Bashir, MPhil (PhD student) Multiplicative ideal theory, factorization theory, zero-sum theory
Laura Cossu
Laura Cossu, PhD Commutative rings, matrix theory, factorization theory
Özgür Esentepe
Özgür Esentepe, PhD Commutative Algebra, Representation Theory
Alfred Geroldinger
Alfred Geroldinger, Ao. Univ.-Prof. Multiplicative ideal theory, factorization theory, additive combinatorics, zero-sum theory
Felix Gotti
Felix Gotti, Fulbright Nawi Graz Visiting Professor Algebra, Combinatorics
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Florian Kainrath, Ass.-Prof.
Zahra Nazemian
Zahra Nazemian, PhD Module theory, Noncommutative algebra and ring theory, Homological algebra and its application in ring theory
Nebojsa Pavic
Nebojsa Pavic, PhD Algebraic geometry, singularities, homological algebra and derived categories
Mara Pompili
Mara Pompili, Dott. Mag. (PhD student)
Balint Rago
Balint Rago, MSc (PhD student)
Andreas Reinhart
Andreas Reinhart, Priv.-Doz. Commutative rings, multiplicative ideal theory, factorization theory
Gülşen Ulucak
Gülşen Ulucak, Visiting Professor Commutative ring, module theory and lattice theory (supported by 2219-International Postdoctoral Research Fellowship Program of The Scientific and Technological Research Council of Turkey)
Qinghai Zhong
Qinghai Zhong, Research Associate Additive Combinatorics and Combinatorial Factorization Theory

Former Members

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