RAND-COMB-DESIGN · Random Combinatorial Designs

The objective of this proposal is to develop fundamental and influential research into combinatorial designs. These objects have fascinated pure mathematicians for over 200 years and have also found many applications, for example in biological experiment design or in the design of strong error correcting codes in order to transmit data securely. The majority of research in design theory has focused on the existence and construction of designs. However recent breakthroughs have opened up exciting new perspectives, allowing for a much deeper understanding of these objects. The aim of this project is to develop these new directions by adopting a probabilistic stance and studying random designs. Our key objectives explore the existence and statistics of global structures in large designs and the longstanding problem of efficient algorithms for random sampling of designs. Through this, the project will foster connections between areas of pure mathematics, in particular extremal and probabilistic combinatorics, and the field of randomized algorithms in theoretical computer science. In order to achieve the proposal's objectives, the researchers will build upon a range of powerful novel methods, drawing on the expertise of the experienced researcher in absorption techniques and spanning structures and that of the host in rainbow structures and Markov chains. This will foster an exchange of knowledge between the two parties and greatly enhance the research potential of the experienced researcher. This project thus provides a pivotal opportunity for the development of his career as a young scientist, enabling him to push this exciting branch of design theory forward, broaden his knowledge and cement himself as a prominent researcher in several disciplines.