Discrete Mathematics

Discrete Mathematics is an important part of modern mathematics that comprises the complete spectrum from pure to applied mathematics. In the mathematical landscape of Styria, multifaceted research in discrete mathematics is certainly one of the significant features that links the mathematical competences present at Graz University (Karl- Franzens-Universität Graz), Graz University of Technology (TU Graz) and University of Leoben (Montanuniversität Leoben), with multiple interactions between these three institutions. In the present DK-plus we want to unite the present knowledge in order to establish a joint, specific, advanced doctoral program in Discrete Mathematics at those three Universities. Following a current trend, we can formulate our mission and vision as "Advanced mathematical education through advanced mathematical research and advanced mathematical research through advanced mathematical education." The main ingredients of the program are an intensive mentoring system, a curriculum consisting of lectures and seminars in which the students get the opportunity to present their results in front of the entire DK faculty, as well as an extensive exchange program which gives the PhD students the possibility to get acquainted and establish close contacts with the international scientific comunity. This exchange comprises the invitation of visiting professors from abroad, the organisation of conferences and workshops as well as the participation in international conferences. Moreover, each of the students has to work at an international research group abroad for a total of at least one semester. The common activities within the program, such as the Discrete Mathematics Seminar and the yearly Discrete Mathematics Day (and more) aim also at creating a common spirit ("corporate identity") among all members (students and staff) of the DK-plus that lasts beyond the PhD graduation. In the present DK-plus 10 scientists from the three universities take part. They are externally supported by 2 associated scientists. Many different aspects of Discrete Mathematics are covered: combinatorial, additive and algorithmic number theory, discrete dynamics and fractals, algebraic structures, graph theory, ergodic theory, harmonic analysis and spectral theory, discrete stochastics, analysis of algorithms, cryptography, combinatorial optimisation, discrete applied geometry, and more. All these are fields of expertise of the participating scientists. The variety of topics is augmented by the intensive guest program.