Trends in Mathematics

The present volume collects extended abstracts of lectures and talks presented at the Summer School and Conference &quote;Analysis, PDEs and Applications&quote; held 24 June - 6 July 2024 at Yerevan State University, Armenia. The thematic scope of contributions includes linear and non-linear partial differential equations, spectral theory and microlocal analysis, harmonic and functional analysis, theory of functions and approximation theory, and applications in mathematical physics. Each talk or lecture begins with a survey of a body of mathematical work, either classic or modern, leading up to recent advances. This is followed by an exposition of either a specific research problem or a broader area of modern mathematical research, presented by an expert in the field.The volume will be of interest to not only students and young researchers, but also experts looking for a crash course in the main concepts and ideas in one of the many advanced mathematical topics discussed.