Mathematic moments

From 11 to 14 March 2024, Research Fellows Philipp di Dio (main organiser / Mathematics) and Tobias Sutter (co-organiser / Computer and Information Science) organised the conference “Moments and Polynomials: Applications and Theory 2024” (MoPAT-24).

Philipp di Dio works on the interplay between moments, polynomials and partial differential equations. His former doctoral supervisor Konrad Schmüdgen, who is a Senior Fellow and was at the Zukunftskolleg from January to March 2024, helped with the preparations and joined the conference as well. Thanking him for their intensive collaboration, Philipp di Dio pointed out the importance of Konrad Schmüdgen’s work for the conference topic. “With his main research in ‘Operator Theory’, Konrad Schmüdgen achieved a major breakthrough in the late 1990s and played an essential role in his research area, in which he studied and taught for decades. This resulted in several books and numerous high-level articles and led to subsequent studies by several algebra groups in Konstanz that are actively working on projects initiated by Schmüdgen’s accomplishments,” says Philipp di Dio, summarising Schmüdgen’s achievements.

Tobias Sutter has been a tenure-track professor for computer science with a focus on machine learning at the University of Konstanz since 2021. After postdoctoral research positions at EPFL in Lausanne and ETH Zürich, he is now both a fellow at the Zukunftskolleg and group leader at the Cluster of Excellence “Centre for the Advanced Study of Collective Behaviour”, as well as a member of the Programme Committee of the Annual Learning for Dynamics & Control Conference (L4DC). His research focuses on machine learning, stochastic optimisation, and control and information theory.

The aim of MoPAT-24 was to bring both aspects together, i.e. the interplay and connection between the theory of moments and polynomials, by looking at past, present and future developments. The topics covered not only the classical theory of moments and polynomials but also looked at matrix moments and polynomials as well as applications. 

“The conference highlighted the recent progress in moments and polynomials, reaching from theory of (multivariate) polynomials and matrix polynomials to applications in optimisations,” summarises Philipp di Dio.

During the 4-day conference, the invited speakers from universities in England, France, the Netherlands, Austria, Switzerland, Italy, Poland, Slovenia, Norway, Morocco and Germany gave over 30 talks to an audience of more than 40 participants. A list of participants and abstracts can be found here.

Alongside the compelling talks, the conference programme included an excursion to Hohentwiel Castle in Singen, which took place in the afternoon of 12 March. On 13 March, a conference dinner took place at Comturey, a restaurant on Mainau Island. “During the excursion to Hohentwiel and the conference dinner on Mainau Island, we were fortunate to continue the discussion about current developments in mathematics,” says Philipp di Dio.