In mathematics, a fundamental pursuit is the classification of mathematical objects, such as set, shapes, and functions, in a way that captures their essential characteristics without redundancy. This endeavor relies on the notion of invariants, which, akin to barcodes, encapsulate essential characteristics of these entities. For quantum spaces, this classification presents several challenges and has progressed only on a case-by-case basis. We strive to understand the structure and invariants of these spaces across a broader spectrum. To achieve this, we follow the mathematical principle of duality and employ the tools of noncommutative geometry—a discipline profoundly influenced by quantum theory.

Mathematical models for the emergence of structures such as rings, spirals and waves in nature are typically based on an idealized world, where random disturbances and complicated spatial structures are ignored. The researchers will develop a framework to describe such effects in a precise fashion, which will allow us to actually include them in our models.

This conference unites algebraic geometry researchers from the Netherlands, UK, France, and Belgium. Algebraic geometry studies geometric spaces defined by polynomial equations, from simple curves like circles and parabolas to complex higher-dimensional structures. The field develops algebraic tools to analyze these spaces intrinsic properties. With sustainability in mind, this event fosters a lasting research community connected by high-speed rail. In-person collaboration is vital in pure mathematics, but climate change necessitates sustainable academic practices. These nations are well-connected by Eurostar, making this conference a pilot for an annual event rotating among the four countries, exclusively using sustainable travel.

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Statistical learning is everywhere: from movie recommendations to text analysis. Despite high expectations surrounding statistical learning, it oftentimes provides unreliable performance in applications. Fraudsters try to mislead algorithms and medicine is data-scarce, which leads to high variance. To tackle the challenges in statistical learning I will use tools from interactive decision-making. Contrary to statistical learning interactive decision making is a dynamic setting that does not rely on restrictive assumptions for strong guarantees. I aim to provide solid mathematical foundations to understand underlying mechanisms and guarantee optimal performance at deployment. Ultimately satisfying the high expectations with low variance.