Herbert Edelsbrunner Awarded ERC Advanced Grant

In the latest round of funding awards, Herbert Edelsbrunner, a mathematician and computer scientist, received an ERC Advanced Grant. With an average success rate of around 12%, these grants are a testament to the quality of the work of those who receive them, as well as the innovation and expected impact of their research plans. Edelsbrunner, a professor at the Institute of Science and Technology Austria (IST Austria) since 2009, uses topology, algorithms, and computer software to answer questions related to the recognition, matching, and classification of shape that arise in a variety of applications, from scientific visualization to molecular structure.

ERC grants provide long-term funding for ground-breaking, curiosity-driven research, and Edelsbrunner’s project is no exception. In his project, “Alpha Shape Theory Extended”, he will work to fully develop a larger theory that unites several of the topics that he has worked on before: alpha shapes, wrap complexes, and persistent homology.

Alpha shapes are way of connecting points defined by Edelsbrunner and his collaborators in the 1980s, and they played a key role in sophisticated analyses of molecular structures. The wrap complex was instrumental in getting fast and accurate geometric software for surface reconstruction that emerged in the late 1990s.

Alpha shapes and wrap complexes motivated Edelsbrunner’s work developing persistent homology, a method for determining topological features at different scales. Persistent homology is the most important method in topological data analysis (TDA), and—given its increasing reach, complexity, and versatility—is likely to remain so in the future. A framework unifying these concepts would broaden and deepen the existing theory, and enable new applications in science, including medicine and biology, as well as to abstract or very high-dimensional data, such as text or language. For instance, Edelsbrunner, together with students and other collaborators, is already working on text applications and developing the necessary extensions in TDA.

Thomas Henzinger, President of IST Austria, congratulates the awardee: “Herbert Edelsbrunner’s work exemplifies both the high quality and the interdisciplinary nature of the research performed on campus, and I look forward to seeing further connections between the mathematical and experimental sciences—one of the Institute’s characteristic strengths.”