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Explore the mathematical foundations of kinematic varieties through the lens of Gram matrices in this advanced lecture delivered at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the intricate connections between algebraic geometry and amplitudes as part of a comprehensive thematic programme examining these mathematical structures. Learn how Gram matrices serve as fundamental tools in understanding kinematic varieties, building upon previous foundational concepts to develop deeper insights into their geometric and algebraic properties. Examine the theoretical framework that connects these mathematical objects to broader applications in physics and mathematics, particularly in the context of scattering amplitudes and their geometric interpretations. Gain exposure to cutting-edge research methodologies and mathematical techniques used to analyze these complex algebraic structures, presented by a leading expert in the field of algebraic geometry and its applications to mathematical physics.
