Cluster Algebras and the Geometry of Scattering Amplitudes

Mar 3, 2020, 9:00 AM → Mar 5, 2020, 6:00 PM UTC

Higgs Centre Seminar Room

The aim of this meeting is to bring together physicists and mathematicians who are interested in the connections between cluster algebras and the geometry of scattering amplitudes. This is intended to facilitate increased interaction and collaboration between these fields, and to provide an avenue for the articulation of interesting and concrete mathematical problems whose resolutions promise to lead to novel physical insights and combinatorial methods. Specific topics to be discussed include:

• the positive grassmannian

• cluster adjacency

• cluster polylogarithms

• tropical grassmannians

• cluster polytopes

• the analytic structure and kinematic geometry of nonplanar amplitudes

• geometric aspects of worse-than-polylogarithmic amplitudes

In particular, it is hoped that the program will stimulate new ideas for how cluster-algebraic techniques can be used to understand the analytic structure of scattering amplitudes beyond the polylogarithmic sector of planar N=4 super-Yang-Mills theory. Please click on speakers' names to view their talks:

• Nima Arkani-Hamed

• Jacob Bourjaily

• Steven Charlton

• James Drummond

• Nick Early

• Anna Felikson

• Mikhail Gekhtman

• Johannes Henn

• Tomasz Lukowski

• Georgios Papathanasiou

• Marcus Spradlin

• Cristian Vergu

 

Accommodation

 

Please follow this link to view available B&Bs and guesthouses close to the Kings Building Campus and the James Clerk Maxwell Building. Please inquire about academic rates. Further information on the venue can be found here.

Organisers

• Herbert Gangl 

• Einan Gardi

• Ömer Gurdogan

• Andrew McLeod

Advisory Committee

• Jacob Bourjaily 
• Marcus Spradlin
• Anastasia Volovich

 

Tuesday, March 3

9:00 AM → 10:00 AM Jacob Bourjaily - Stratifying On-Shell Cluster Varieties

Jacob Bourjaily.pdf

10:00 AM → 11:00 AM Coffee

11:00 AM → 12:00 PM Anna Felikson - Quiver mutations, reflection groups and curves on punctured disc

Anna Felikson.pdf

12:00 PM → 1:30 PM Lunch

1:30 PM → 2:30 PM Marcus Spradlin - Cluster Algebras and SYM Theory

Marcus Spradlin.pdf

2:30 PM → 3:30 PM Coffee

3:30 PM → 4:30 PM Mikhail Gekhtman - Periodic staircase matrices and generalized cluster algebras

Wednesday, March 4

9:00 AM → 10:00 AM James Drummond - Cluster algebras, tropical Grassmannians and Amplitudes

10:00 AM → 11:00 AM Coffee

11:00 AM → 12:00 PM Nick Early - From matroid subdivisions of hypersimplices to generalized Feynman diagrams

Nick Early.pdf

12:00 PM → 1:30 PM Lunch

1:30 PM → 2:30 PM Georgios Papathanasiou - How tropical are scattering amplitudes?

2:30 PM → 3:30 PM Coffee

3:30 PM → 4:30 PM Tomasz Lukowski - From amplituhedron to positive tropical Grassmannian via hypersimplex

Tomasz Lukowski.pdf

Thursday, March 5

9:00 AM → 10:00 AM Johannes Henn - A simple algorithm for finding canonical differential equations for Feynman integrals

10:00 AM → 11:00 AM Coffee

11:00 AM → 12:00 PM Cristian Vergu - Progress in N=4 scattering amplitudes computations

Cristian Vergu.pdf

12:00 PM → 1:30 PM Lunch

1:30 PM → 2:30 PM Steven Charlton - Cluster Polylogarithms

Steven Charlton.pdf

2:30 PM → 3:30 PM Coffee

3:30 PM → 4:30 PM Nima Arkani-Hamed

Nima Arkani-Hamed.pdf