Combinatorics and geometry related to scattering amplitudes

Winter 2026, we are having a learning seminar on combinatorics and geometry related to scattering amplitudes. This includes things like positroids, Grassmannians, total positivity, scattering amplitudes as they build the amplituhderon and otherwise. One particular direction of interest is connections to the web approach to SLr invariants (that some of us are experts on (not me)). However, this is a learning seminar, where most of the weeks will consist of a non-expert explaining something to the rest of us with the goal that we all understand more than before, the speaker most definitely included. We will hear directly from experts only from time to time.

We will meet Tuesdays at 10:30am in the Alice room at Perimeter Institute (at least until March 3). Note the time change from the first week in order to accommodate some departmental obligations.

Schedule

January 13 at 10:00am
Ren Yeats, combinatorial aspects of positroid background
January 20
Oliver Pechenik, connections to SL3 webs and other web background
January 27
Mykola Semenyakin, some positivity and positive geometry things
February 3
Kledion Shahini, intro to scattering amplitudes from this perspective
February 10
Kledion Shahini, scattering amplitudes part 2
February 17
No learning seminar on account of reading week
February 24
Mike Cummings, geometry of the amplituhedron
March 3
Ian George, more scattering amplitude connections
March 10
Sonja Klisch, more on BCFW and on-shell diagrams
March 17 in Space
Ian George, continuing the explicit link between the on-shell diagrams and the grassmannian
March 24 in Space
Ren Yeats, some kind of introduction to the momentum amplituhedron
March 31
Michael Borinsky, connections to alternating sign matrices
April 7
Stephan Pfannerer
April 14
April 21

References

  • The combinatorial geometry of particle physics by Thomas Lam
  • Positroid notes by Thomas Lam
  • Combinatorics of positroids Suho Oh
  • An invitation to positive geometries Thomas Lam
  • Positive geometries and canonical forms Nima Arkani-Hamed, Yuntao Bai, Thomas Lam
  • Scattering Amplitudes and the Positive Grassmannian, Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, Jaroslav Trnka.
  • BCFW tilings and cluster adjacency for the amplituhedron Chaim Even-Zohar, Tsviqa Lakrec, Matteo Parisi, Melissa Sherman-Bennett, Ran Tessler, Lauren Williams
  • Amplituhedra and origami Pavel Galashin
  • Total positivity, Grassmannians, and networks Alexander Postnikov
  • Total positivity: tests and parametrizations Fomin and Zelevinsky
  • The Amplituhedron BCFW Triangulation Chaim Even-Zohar, Tsviqa Lakrec, Ran J. Tessler
  • The positive Grassmannian, the amplituhedron, and cluster algebras Lauren Williams
  • The momentum amplituhedron David Damgaard, Livia Ferro, Tomasz Lukowski, Matteo Parisi
  • The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron Tomasz Lukowski, Matteo Parisi, Lauren K. Williams

    Previous learning seminars

    Learning seminars from my time at Simon Fraser University. (I wonder how long these links will work.)

    Older seminars on more motivic topics from when I was at Boston University. There are many broken links, but I consider these archived and so they will not be changed.