题 目: Transfinite Barycentric Coordinates for Arbitrary Planar Domains
报告人: Kai Hormann Professor
Università della Svizzera italiana
Faculty of Informatics
摘 要: In the paradigm of quantum measurement, complete mutually unbiased bases (MUBs) and symmetric informationally complete positive operator valued measures (SIC-POVMs) are two prominent objects due to their structural symmetry and remarkable features. However, their existences in arbitrary dimensions (Zauner's conjectures) remain elusive. We discuss some aspects in the pursuing and constructing of MUBs and SIC-POVMs via group frames and magic states. We highlight the key roles played by the orbit of Heisenberg-Weyl group and certain mystical fiducial states (vectors in finite dimensional Hilbert spaces), which are most magic. Some related open problems are also presented.
简介: Kai Hormann is a full professor in the Faculty of Informatics at the Università della Svizzera italiana (USI) in Lugano, Switzerland. His research interests are focussed on the mathematical foundations of geometry processing algorithms as well as their applications in computer graphics and related fields. In particular, he is working on generalized barycentric coordinates, subdivision of curves and surfaces, barycentric rational interpolation, and dynamic geometry processing. Professor Hormann has published over 100 papers in the professional literature and is an associate editor of the journalsComputer Aided Geometric Design and Dolomites Research Notes on Approximation. He served as chair of the SIAM Activity Group on Geometric Design in 2017/2018 and is entrusted with the chairmanship of the steering board of the international conference Geometric Modeling and Processing (GMP) since 2017. In June 2024, he received the John A. Gregory Award for his fundamental contributions to and the lifetime impact on the field of geometric modeling.
报告时间：2025年4月1日周五9:00-10:00
报告地点：6教南528
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