Project 03: "Additive group theory, zero-sum theory and non-unique factorizations"

This project is running since 2010.

Principal investigator: Alfred Geroldinger
University of Graz, Austria.
Mentor for: McMahon; Barroero, Kreso, Weitzer.

Associated scientist: Karin Baur (2012-2014)
University of Graz, Austria.
She is now principal investigator of project 12.

DK Student

  • Second phase of the doctoral program:
  • JunSeok Oh (Republic of Korea; since October 2015)
    Email: junseok.oh@uni-graz.at
    Mentors: Karin Baur, Andreas Reinhart.
  • First phase of the doctoral program:
  • Daniel Smertnig (Austria; March 2011–May 2014)
    Personal homepage; Email: daniel.smertnig@uni-graz.at
    Mentors: Christian Elsholtz, Robert Tichy.
    PhD Defense: May 22, 2014.
    Referees: A. Facchini (Padova), A. Geroldinger, A. Loper (Ohio).
    Examiners: A. Facchini (Padova), A. Geroldinger

Project description (pdf-file)

One of the main areas of the research of A. Geroldinger is combinatorial and additive number theory. In particular, his research centers on zero-sum theory in abelian groups. Main methods in this area stem from additive group theory including all type of addition theorems. Another important topic in Geroldinger's research activities are non-unique factorisations in monoids and integral domains. The main objective here is a systematic treatment of phenomena related to the non-uniqueness of factorisations in structures of arithmetical interest. The main focus lies on principal and non-principal orders in algebraic number and function fields, Mori domains, Krull monoids and congruence monoids. The methods are algebraic, combinatorial and analytic. Moreover, Geroldinger is interested in the structure and ideal theory of commutative rings and monoids. At present he investigates the (arithmetic and ideal theoretic) structure of congruence monoids, C-monoids and their various generalisations.