The Algebra, Geometry and Computer Algebra Group (AGAG) focusses on fundamental research in classical key areas of pure mathematics and on modern applications thereof. The main focus is on Algebraic Geometry, Representation Theory, Number Theory and, in the area of applications, on Cryptography. Within the research focus particular emphasis is put on algorithmic aspects of the aforementioned areas respectively algorithmic questions that result from the cross-linking of these areas with other topics within or beyond mathematics.

The research profile of the AGAG is characterized by many national and international collaborations, excellent scientific publications, and by well-established broad focusing.

The excellent international reputation of the AGAG has been emphasized by the ERC Advanced Grant that has been awarded to Prof. Dr. G. Malle in 2011. Moreover, the federal coordinated priority programme "Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory" (SPP 1489, running 2010-2016) of the German Research Foundation (DFG) was coordinated by Prof. Dr. W. Decker.

SFB-TRR 195 "Symbolic Tools in Mathematics and their Application"

The German Research Foundation (DFG) has decided to fund a new trans-regional collaborative research centre (SFB-TRR) "Symbolic Tools in Mathematics and their Application" coordinated by TU Kaiserslautern (Spokesman: Prof. Dr. G. Malle) starting in January 2017. In the SFB-TRR scientists of the Algebra, Geometry and Computer Algebra Group collaborate with scientists at RWTH Aachen University, Saarland University (both co-applicant institutions), TU Berlin, and the Universities of Siegen, Stuttgart and Tübingen. The substantial participation of the members of the AGAG in the SFB-TRR 195 documents the close collaboration within the AGAG as well as outstanding strength of research focus on algorithmic aspects.

The Computer Algebra System SINGULAR

The Computer Algebra System SINGULAR developed in Kaiserslautern is the internationally leading Open Source System for polynomial computations in mathematical science and practical applications. Its world wide distribution is well-documented by hundreds of references in scientific publications in mathematics, but also in engineering and natural sciences and in medicine. Besides its relevance for national and international scientific collaborations, SINGULAR is also the basis for collaborations of the AGAG with other faculties of TU Kaiserslautern and with the Fraunhofer ITWM (Competence Center High Performance Computing).