Mathematics Research Reports is a journal run for and by mathematicians, committed to the mission of providing high-quality scientific content, while adhering to the principles of Fair Open Access. This includes being freely available for a scientific audience worldwide, with no author publication charges, thanks to support from the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University. This journal publishes research announcements of significant advances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). All articles should be designed to communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. All papers are reviewed, and the entire Editorial Board must approve the acceptance of any paper. Founded by members of the editorial board of Electronic Research Announcements in Mathematical Sciences (published by the American Institute of Mathematical Sciences and preceded by Electronic Research Announcements of the American Mathematical Society), Mathematics Research Reports is owned and operated by its editorial board, and supported by senior editors drawn from among former editors of both Electronic Research Announcements in Mathematical Sciences and Electronic Research Announcements of the American Mathematical Society.