Applied Discrete Mathematics
Principal Investigator: Miklós Maróti
The tremendous advances in the development of efficient computer hardware and architectures (vast amount of compute power and storage in the cloud, very efficient general purpose vectorized computation on the GPU) and the availability of freely available scientific computation libraries (computer algebra systems, theorem proves, SAT and SMT solvers, deep neural networks) have propelled all engineering and applied scientific fields in the last decade. This progress presents unique challenges and opportunities to mathematicians: 1) to study the applicability and limitations of these architectures and algorithms aiding practitioners, and 2) to use these new architectures and algorithms within mathematics to attack unsolved problems.
To focus our efforts and to properly employ the expertise present at the Department of Mathematics at the University of Szeged, we have selected a handful of discrete problems where concentrated effort can yield significant theoretical advances with possible applications. These are 1) SAT solvers and their relation to algebra and clone theory, 2) graph embedding problems of practical sizes where the Regularity Lemma of Szemeredi cannot be applied, and 3) applicability of continuous methods and deep neural networks for discrete problems.
Béla Csaba, Miklós Dormán, Péter Hajnal, Kamilla Kátai-Urbán, Gábor P. Nagy, Gábor V. Nagy, László I. Szabó, Nóra Szakács, Tamás Waldhauser, László Zádori