BIRS workshop: Combinatorial and Geometric Discrepancy

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computational geometry discrete mathematics dynamical systems

Banff International Research Station

Audience: Researchers in the topic
Conference dates: 30-Sep-2020 to 02-Oct-2020
Curator: BIRS Programme Coordinator*
*contact for this listing

Discrepancy theory is concerned with the existence and the construction of configurations which exhibit a high degree of regularity or uniformity. A classical example is the case of finite point sets in Euclidean space, where the degree of regularity is measured by comparing the number of points contained in an axis-parallel test box to the volume of the box, and then taking the maximal deviation among all test boxes. The notion of discrepancy has been generalized to many different settings and the concept has been fruitfully used in convex and computational geometry, numerical analysis, combinatorics and theoretical computer science, to name just a few areas. For example the notion of discrepancy with respect to boxes above is closely related to combinatorial discrepancy, which is itself closely related to vector balancing problems amenable to tools from geometric convex analysis. These connections also raise algorithmic questions, which have seen much recent progress again using tools from geometry and high-dimensional probability. Another example of connections between discrepancy and other areas of mathematics is provided by constructions of low-discrepancy sequences using orbits of ergodic maps, with connections to Teichmueller theory and classical ergodic theory.

Unfortunately, sometimes these various connections are underexplored because of insufficient interaction between different communities. With the current workshop, we will bring together leading scientists from different mathematical disciplines working on discrepancy-related problems, to present their work and methods in a way which is accessible for mathematicians from other disciplines. We further invite young researchers to participate. They will be presented with a wide panorama of discrepancy-related topics in an attractive and accessible way. Our goal is for the workshop to lead to new and fruitful collaborations across old-established borders of mathematical communities, and have a lasting impact on the development of many young researchers.

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