Course Identification

First degree in math or physics

Throughout the course we will study new mathematical techniques for scattering amplitudes of quantum field theories. A tentative list of subject (which may vary):

-The positive Grassmannian and its relation to N=4 SYM and ABJM theories.

-The amplituhedron

-On shell techniques and the BCFW recursion

-Symboles and applications to calculating loop amplitudes in N=4 SYM.

-Cluster algebras and their appearance in scattering amplitudes of N=4 SYM.

-The ABHY associahedron  and bi-adjoint phi^3 theory. 

-The CHY formalism , the double copy formalism.

-Positive geometries and related tropical geometry.

At the end of the seminar the student:

1. will become familiar with the rich mathematics of  the positive Grassmannian, cluster algebras, the amplituhedron, symbols, positive geometries and more.

2. Will relate the above techniques to the study of QFTs.

3. will improve her/his lecturing techniques, and ability to learn new scientific material on her/his own.

A partial and tentative list:

The Grassmannian formalism:

https://arxiv.org/abs/1212.5605

https://arxiv.org/abs/math/0609764

The amplituhedron:

https://arxiv.org/abs/1312.2007

https://arxiv.org/abs/2112.02703

Clusters with relations to physics:

https://arxiv.org/abs/1212.6263

https://arxiv.org/pdf/2310.17727

Symbols:

https://arxiv.org/abs/1006.5703

Positive geometries:

https://link.springer.com/article/10.1007/JHEP11(2017)039

https://www.samuelfhopkins.com/OPAC/files/proceedings/lam.pdf

The ABJM amplituhedron:

https://arxiv.org/abs/2306.00951

Bi-adjoint Phi^3 theory and relation to CHY:

https://arxiv.org/abs/1711.09102

https://arxiv.org/abs/1307.2199

Tropical geometry, CEGM:

https://arxiv.org/abs/1903.08904

https://arxiv.org/abs/2205.02722

https://arxiv.org/abs/2312.12319