Course Identification

Linear algebra.

*Definitions and basic examples of cluster algebras.

*The positive Grassmanian, its stratification and relations with cluster algebras.

*The amplituhedron: definition, conjectures and theorems.

*If time permits: introduction to positive geometries and relations to physics.

The student will become familiar with the basics of cluster algebras positive Grassmanian, the amplituhedron and positive geometries, including some of the most recent works in the field.

-Cluster algebras:

1) "Cluster algebras: an introduction" by Williams - https://arxiv.org/abs/1212.6263.

2) "Introduction to cluster algebras" by Fomin, Williams and Zelevinsky - https://arxiv.org/abs/1608.05735.

-The positive Grassmanian:

"Total positivity, Grassmanians and networks" by Posnikov - https://arxiv.org/abs/math/0609764.

-The amplituhedron:

1) "Scattering amplitudes and the positive Grassmanian" by Arkani-Hamed, Boujaily, Cachazo, Goncharov, Postnikov, Trnka - https://arxiv.org/abs/1212.5605.

2) "The m=2 amplituhedron and the hypersimplex: signs, triangulations, Eulerian numbers" by Parisi, Sherman-Bennet, Williams - https://arxiv.org/abs/2104.08254.

-Positive geometries:

"Positive geometries and canonical forms" by Arkani-Hamed, Bai, Lam - https://arxiv.org/abs/1703.04541.