Course Identification

Title:

A seminar on positive geometries

Code:

20234141

Lecturers and Teaching Assistants

Lecturers:

Prof. Ran Tessler

TA's:

N/A

Course Schedule and Location

Year:

2023

Semester:

First Semester

When / Where:

Tuesday, 14:15 - 17:00, Goldsmith, Rm 208

First Lecture:

08/11/2022

End date:

10/02/2023

Field of Study, Course Type and Credit Points

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

Comments

N/A

Prerequisites

No

Restrictions

Participants:

10

Language of Instruction

English

Attendance and participation

Required in at least 80% of the lectures

Grade Type

Numerical (out of 100)

Grade Breakdown (in %)

Attendance

10%

Assignments:

10%

Seminar:

80%

Evaluation Type

Seminar

Scheduled date 1

Date / due date

N/A

Location

N/A

Time

-

Remarks

N/A

Estimated Weekly Independent Workload (in hours)

3

Syllabus

1)Definition of positive geometries and canonical forms. arXiv:1703.04541

2) Polytopes are positive geometries. arXiv:1703.04541

3) Positive Grassmannian is a positive geometry. arXiv:math/0609764 arXiv:1212.5605, arXiv:1707.02010

4) The amplituhedron and N=4 SYM arXiv:1312.2007, arXiv:2112.02703

5) Loop amplituhedron arXiv:1408.2459

6) Momentum and orthogonal momentum amplituhedron arXiv:1905.04216, arXiv:2111.03037

7) The moduli of disks as a positive geometry. arXiv:math/0606419

8) phi^3, ABHY associahedron and Halohedron arXiv:1711.09102, arXiv:1806.01842

9) Higher scalar theories arXiv:2205.02722arXiv:1811.05904, arXiv:1906.12148

Learning Outcomes

The students will become familiar with the emerging field of positive geometries, its mathematical foundations and relation to physics.

The student will get to know interesting mathematical structures such as polytopes, toric and cluster varieties, associahedra and amplituhedra.

Reading List

N/A

Website

N/A