Recent years have seen the emergence of a surprising array of relationships between scattering amplitudes and ``positive geometries", a formulation of physics where the dictates of spacetime and quantum mechanics--locality and unitarity--are not taken as primary, but rather arise from more primitive mathematical notions. This line of work has exposed new connections between these most basic real-world physical processes, and areas of active current research in mathematics, from cluster algebras to total positivity, tropical geometry to intersection theory. The aim of this series of workshops is to bring together experts in the field for two-day meetings, with pedagogical tutorials and informal discussions on the latest developments.

Planned meetings for 2020/2021 academic year (in virtual setting):

♣ First meeting: September 15-16, 2020

♣ Second meeting: February 8-9, 2021

♣ Third meeting: Spring 2021

Structure of meetings:

♦ First day: tutorials on recent topics, presented in semi-pedagogical way focused on experts in the field

♦ Second day: discussions on projects in progress

Organizers: Nima Arkani-Hamed, Jaroslav Trnka

Second meeting: February 8-9, 2021

Focus of the meeting: Phi^3 amplituhedra/cluster polytopes, geometries for general phi^p theories, new developments around CHY and scattering equations, generalized scattering amplitudes and other topics in this neighborhood. 

Speakers and topics

List of speakers and topics, including background material.

• Nima Arkani-Hamed (All-loop, non-planar tr[phi^3] amplituhedra/"surfacehdra" for Riemann surfaces) 
• Bruno Gimenez Umbert (Generalized Grassmannian scattering amplitudes). https://arxiv.org/abs/1903.08904, https://arxiv.org/abs/1912.09422
• Song He & Prashanth Raman (CHY/generalized permutohedra+binary geometries). https://arxiv.org/pdf/1711.09102.pdf https://arxiv.org/pdf/1912.08707.pdf  https://arxiv.org/abs/2005.07395v2 
• Alok Laddha (Polytopes for phi^p amplitudes at tree and loop level)
• Sebastian Mizera (Stasheff Polytopes, Cosmology, and the Ising Model). https://arxiv.org/abs/1706.08527, https://arxiv.org/abs/1910.11852, https://arxiv.org/abs/2007.06574
• Simon Telen (Likelihood equations and scattering amplitudes). https://arxiv.org/pdf/2012.05041.pdf
• Nick Early (Simple Generalized Feynman Diagrams and a binary geometry on X(3,n)). https://arxiv.org/abs/1912.13513, https://arxiv.org/abs/2010.09708.

Schedule

All times are in EST timezones. 

Monday, Feb 8

• 9:00-10:30: Song He & Prashanth Raman
• 10:45-12:15: Sebastian Mizera
• 12:30-14:00: Simon Telen

Tuesday, Feb 9

• 9:00-10:30: Bruno Gimenez Umbert & Nick Early
• 10:45-12:15: Alok Laddha
• 12:30-14:00: Nima Arkani-Hamed

Zoom links

Monday, Feb 8: https://ucdavis.zoom.us/j/97509879328

Tuesday, Feb 9: https://ucdavis.zoom.us/j/95287052127

First meeting: September 15-16, 2020

Focus of the meeting: Positive geometry for planar N=4 SYM theory, Amplituhedron recent developments, Yangians and symbol letters.

Topics

First day, Sep 15: tutorials on selected topics (1.5 hours each)

• Non-perturbative N=4 geometry by Fernando Alday, Nima Arkani-Hamed, refs: https://arxiv.org/pdf/0903.4707.pdf, https://arxiv.org/pdf/1002.2459.pdf.
• Momentum Amplituhedron by Tomek Lukowski, Livia Ferro; refs: https://arxiv.org/abs/2007.04342
• Qbar equation by Song He, Chi Zhang; refs: https://arxiv.org/pdf/1112.1060.pdf, https://arxiv.org/abs/1911.01290.

Second day, Sep 16: discussions on recent developments (1 hour each)

• Amplituhedron: local triangulations and the dual, lead by Cameron Langer, Minshan Zheng, Enrico Herrmann, Jaroslav Trnka; refs: https://arxiv.org/abs/2007.12191, https://arxiv.org/abs/2009.05607.
• m=2 Amplituhedron, hypersimplices and tropical Grassmannians, lead by Lauren Williams, Mateo Parisi, Tomek Lukowski; refs: https://arxiv.org/abs/2002.06164.
• Yangian invariants and symbol letters, lead by James Drummond, Mark Spradlin, Song He, Andrew McLeod, refs: 1910.14224, 1912.08217, 2007.00646, 2007.01574.
• IR finite objects from four point Amplituhedron, lead by Nima Arkani-Hamed, Johannes Henn, Jaroslav Trnka, refs: https://arxiv.org/abs/1301.0149, https://arxiv.org/abs/1312.7878.

Schedule

All times are in EST timezones.

Tuesday, Sep 15 (tutorials)

• 9:00-11:00: Song He & Chi Zhang
• 11:15-13:00: Tomek Lukowski & Livia Ferro
• 13:15-17:00: Fernando Alday & Nima Arkani-Hamed

Wednesday, Sep 16 (discussions)

• 9:00-10:30 Yangian invariants I
• 10:45-11:45 m=2 Amplituhedron
• 12:00-14:00 Yangian invariants II
• 14:15-16:00 Local triangulations of Amplituhedron
• 16:00-18:00 IR finite from Amplituhedron

Zoom links:

Tuesday, Sep 15: https://ucdavis.zoom.us/j/98630924888

Wednesday, Sep 16: https://ucdavis.zoom.us/j/95260960110

The meeting went great!