Amplituhedra III - Combinatorics and Geometry for m=1,2

Explore the intricate mathematical structures of amplituhedra through this advanced lecture focusing on combinatorics and geometry for cases where m=1 and m=2. Delve into the sophisticated interplay between algebraic geometry and particle physics amplitudes as presented by Melissa Sherman-Bennett from the Erwin Schrödinger International Institute for Mathematics and Physics. Examine the geometric properties and combinatorial aspects of these mathematical objects that have revolutionized our understanding of scattering amplitudes in theoretical physics. Learn about the specific characteristics and computational techniques relevant to low-dimensional cases of amplituhedra, building upon foundational concepts to understand how these geometric structures encode physical information about particle interactions. Gain insights into cutting-edge research connecting pure mathematics with theoretical physics through detailed analysis of these remarkable geometric objects and their applications in modern amplitude theory.