Sum of Squares, Positivity and Property (T) - Lecture 1

Explore the fundamental concepts of Sum of Squares, Positivity, and Property (T) in this 50-minute lecture delivered by Marek Kaluba at the International Centre for Theoretical Sciences. Part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program, this lecture delves into advanced mathematical topics with applications in algebraic and differential geometry, combinatorics, and related fields. Gain insights into the latest developments in the theory of arithmetic and Zariski-dense subgroups, and discover how these concepts connect to long-standing problems in mathematics. Suitable for researchers and advanced students in mathematics, this lecture offers a deep dive into cutting-edge mathematical techniques and their wide-ranging implications.