Seminar on Webs

Time: TBD

Location: TBD

Organizers: Grant Barkley, Elisabeth Bullock, Amanda Burcroff 

About:  This is a learning seminar on webs.  Webs arise in the problem of characterizing the dual vector space of invariant tensors Inv(V1 ⊗ V2 ⊗ . . . ⊗ Vn) under the action of some compact group or simple Lie algebra. Roughly speaking, a web is a certain planar graph that captures operations on such invariant spaces.

Some of the main sources for this seminar will include the foundational   "Spiders for rank 2 Lie algebras" by Greg Kuperberg and also "Tensor diagrams and cluster algebras" by Sergey Fomin & Pavlo Pylyavskyy.  Later talks may focus on more recent research depending on participant interest.  See below for more related materials.

For each meeting, we will decide on a topic, speaker, and relevant sources.  Participants are encouraged to look at the source  material in preparation, but presentations should be designed so that they can be followed with no prior knowledge of that week's material.  Talks will usually last around 40-50 minutes to allow time for questions and discussion.

Sources

• Tensor diagrams and cluster algebras, Sergey Fomin & Pavlo Pylyavskyy

• Spiders for rank 2 Lie algebras, Greg Kuperberg

• Rotation-invariant web bases from hourglass plabic graphs, Christian Gaetz, Oliver Pechenik, Stephan Pfannerer, Jessica Striker, Joshua P. Swanson

  • FPSAC version

• The invariant theory of binary forms, Joseph  P. S. Kung & Gian-Carlo Rota

• Total positivity, Grassmannians, and networks, Alexander Postnikov

• Lie Groups, Lie Algebras, and Representations, Brian Hall

Obligatory picture to make this all more enticing.  What does it mean? Let's find out together. (Source: "Spiders for rank 2 Lie algebras," Kuperberg)