Einsiedler, Manfred; Ward, Thomas Homogeneous dynamics: a study guide. (English) Zbl 1364.37007 Cheng, Shiu-Yuen (ed.) et al., Introduction to modern mathematics. Somerville, MA: International Press; Beijing: Higher Education Press (ISBN 978-1-57146-305-0/pbk). Advanced Lectures in Mathematics (ALM) 33, 171-201 (2015). Summary: These notes give a summary of the course “Ergodic Theory and Applications in Number Theory” at the Summer School in Modern Mathematics at the Tsinghua University in Beijing, June 23–27 (2013). As in the summer school, we will need to be brief at times and refer to the references for a detailed treatment. Nonetheless we wish to survey some results and ideas on a close to geodesic journey from the most basic concepts of ergodic theory to some more sophisticated and recent results in homogeneous dynamics.For the entire collection see [Zbl 1326.00080]. Cited in 1 Document MSC: 37A17 Homogeneous flows 37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory 11J13 Simultaneous homogeneous approximation, linear forms 11J25 Diophantine inequalities 22D40 Ergodic theory on groups 22E40 Discrete subgroups of Lie groups 37A35 Entropy and other invariants, isomorphism, classification in ergodic theory 37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010) 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) Keywords:ergodic theory; number theory; homogeneous dynamics PDFBibTeX XMLCite \textit{M. Einsiedler} and \textit{T. Ward}, Adv. Lect. Math. (ALM) 33, 171--201 (2015; Zbl 1364.37007)