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The XIII International Symposium on Quantum Theory and Symmetries (QTS-13), organized by the International Center for Advanced Studies and Physics Department of the Yerevan State University will be held in Yerevan, Armenia on 28 July - 1 August, 2025. The Symposium QTS-13 is dedicated to the memory of George Pogosyan. The purpose of the Conference is to bring together scientists who knew Professor George Poghosyan personally and work with him, or who were influenced by his work. The QTS is one of the traditional conference series taking place each odd years and bringing together the physicists and mathematicians working on the topics of symmetry, including the geometrical methods (classical and non-commutative), groups theory, Lie and nonlinear algebras, in the framework of its possible application in modern quantum physics. The first QTS Symposium was held in Goslar in 1999 and afterward continued in Krakow (2001), Cincinnati (2003), Varna (2005), Valladolid (2007), Lexington (2009), Prague (2011), Mexico City (2013), Yerevan (2015), Varna (2017), Montreal (2019) and Prague (2023).