[NTU-NCTS String Seminar] Amplituhedra and Cluster Algebras

Title:[NTU-NCTS String Seminar] Amplituhedra and Cluster Algebras
Speaker:Dr. Matteo Parisi (IAS, Princeton, and Harvard CMSA)
Time: July. 17, 2023 (Mon.) 10:00-11:00
Venue: Rm. 815, Dept. of Physics, NTU

In this talk, we will discuss how two objects of great interest to both mathematicians and physicists are connected. On one hand, Amplituhedra are the image under a linear map of the positive part of the Grassmannian -- where all the pluckers are nonnegative. Introduced by physicists to encode the probability of particle interactions -- scattering amplitudes -- in a certain Quantum Field Theory, they are semialgebraic sets which generalise polytopes inside the Grassmannian. On the other hand, Cluster Algebras are a remarkable class of commutative rings introduced by Fomin and Zelevinsky. Many nice algebraic varieties are
known to have a cluster algebra structure, including the Grassmannian. They also emerged in physics in the context of scattering amplitudes, where they contributed to both conceptual and computational advances. We will show how Amplituhedra possesses surprisingly rich cluster structures and how they relate to their geometry and combinatorics.