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 SL_r 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: Karen 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: Mike Cummings, something including the word amplituhedron
February 17: No learning seminar on account of reading week
February 24: Michael Borinsky
March 3
March 10
March 17
March 24
March 31
April 7

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

Previous learning seminars

Fall 2025, Matteus ran a learning seminar on the moduli space of graphs and hopefully will have more at that link in future terms too.
Fall 2023, Causal set theory
Fall 2020, Hepp bound reading group
Winter 2019, transseries learning seminar organized by Ali Mahmoud and William Dugan.
Fall 2017 WLD things virtual learning seminar run by Susama Agarwala.
Winter 2017 learning seminar on positroids.

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

Spring 2013 seminar on complex analysis and combinatorics
Fall 2012 complex analysis and combinatorics part I
Fall 2011 multiple zeta values
Summer 2011 the Dynkin operator and renormalization Hopf algebras
Spring 2011 integrable models in combinatorics and physics
In Fall 2010, Samson Black and I organied a learning seminar on knots and quantum field theory.
In late April and May 2010 I gave a series of 5 lectures on Renormalization Hopf Algebras, and the participants kindly took notes.
Spring 2010 workgroup on Random matrices, symmetric functions, and graph enumeration.

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.

Fall 2006 seminar on motives with applications in physics
Spring 2006 Motives-Arithmetic-Physics Seminar (organized by Obi Rej).
Fall 2005 learning seminar on motives