Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory
Emily J. KingUniversität Bremen, Germany
Christopher ManonUniversity of Kentucky, Lexington, USA
Dustin G. MixonThe Ohio State University, Columbus, USA
Cynthia VinzantNorth Carolina State University, Raleigh, USA
Frames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’fand–Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics.
Cite this article
Emily J. King, Christopher Manon, Dustin G. Mixon, Cynthia Vinzant, Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory. Oberwolfach Rep. 15 (2018), no. 4, pp. 2769–2803DOI 10.4171/OWR/2018/46