This volume is dedicated to the memory of Harold Widom (1932-2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time.

It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg-Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area.

The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.

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Estelle Basor is professor emeritus of mathematics at the California Polytechnic State University, and deputy director of the American Institute of Mathematics. Her areas of research are in operator theory and the theory of random matrices.
Albrecht B�ttcher is professor at TU Chemnitz. He is an author of several books and has edited a number of recent books in the Operator Theory series.
Torsten Erhardt is a professor at the UC Santa Cruz. His research interests range from functional analysis over harmonic analysis and Wiener-Hopf factorization theory to complex analysis. Craig A. Tracy is emeritus distinguished professor at UC Davis. His fields of research include statistical physics, integrable systems, and probability theory.

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