# Course Identification

Cluster algebras, positive geometries and the Amplituhedron
20224112

## Lecturers and Teaching Assistants

Prof. Ran Tessler
N/A

## Course Schedule and Location

2022
Second Semester
Tuesday, 14:15 - 17:00, Goldsmith, Rm 208
29/03/2022
19/08/2022

## Field of Study, Course Type and Credit Points

Mathematics and Computer Science: Seminar; Elective; Regular; 3.00 points

N/A

Linear algebra.

12

English

## Attendance and participation

Obligatory

Numerical (out of 100)

10%
10%
80%

Seminar

N/A
N/A
-
N/A

3

## Syllabus

*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.

## Learning Outcomes

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.

N/A