Pavel Galashin

Applets:

*The 2026+ applets were vibe-coded based on my SageMath code.

• Origami-amplituhedron correspondence for Gr(3,6) (2026)
  An origami crease pattern is embedded if and only if the corresponding pair $(\lambda,\tilde\lambda)$ of perpendicular 2-planes belongs to the momentum amplituhedron: see Theorem 1.3 in arXiv:2410.09574v2.
  

• Plabic graphs 2.0 (2026)
  Bounded affine permutations, square moves, zig-zag paths, Le-diagrams, adding/removing bridges, non-reduced plabic graphs, etc.

• Origami reconstruction algorithm (2026)
  Reconstruct an (L-punctured) origami crease pattern from its boundary and puncture locations, illustrating the results of arXiv:2410.09574v2 and arXiv:2606.03439.
  

• Plabic sections of zonotopal tilings (2026)
  View (reduced top-cell) plabic graphs arising as horizontal sections of fine zonotopal tilings of the cyclic 3D zonotope, illustrating the main theorem of arXiv:1611.00492.
  

• Affine permutations game (2024)
  Apply simple conjugations to affine permutations to reduce their length. Based on arXiv:2104.05701 and arXiv:2212.12962.

• Braid variety cluster structures tutorial (html) | Sage code (zip) (2023)
  Sage code for computing double braid variety quivers based on our papers arXiv:2210.04778 and arXiv:2301.07268 with Thomas Lam, Melissa Sherman-Bennett, and David Speyer

• R-systems (2017)
  Sage code for computing the values of the R-system introduced in our paper R-systems with Pavlo Pylyavskyy

• Plabic graphs 1.0 (2015)
  A javascript implementation of the algorithm from the paper
  Weak separation and plabic graphs by Suho Oh, Alexander Postnikov, and David Speyer

Thesis: Totally positive spaces: topology and applications pdf (203 pages). MIT, June 2019.

Research statement (2018): pdf (4 pages)

FPSAC abstracts:

Here you can find extended abstracts to some of my papers, presented at FPSAC by me or my coauthors.

• Critical varieties in the Grassmannian
  A talk given by me at FPSAC 2021 | extended abstract (12 pages) | slides | video (25min)

• Positroids, knots, and q,t-Catalan numbers
  An talk given by Thomas Lam at FPSAC 2021 | extended abstract (12 pages) | slides | video (25min)

• Regularity theorem for totally nonnegative flag varieties
  A talk given by Steven Karp at FPSAC 2020 | slides | video (25min) | extended abstract (12 pages)

• Plabic graphs and zonotopal tilings
  A talk given by me at FPSAC 2018 | slides (25min) | extended abstract (12 pages)

• The totally nonnegative Grassmannian is a ball
  A talk given by Steven Karp at FPSAC 2018 | slides (25min) | extended abstract (12 pages)

• Root system chip-firing
  A talk given by Sam Hopkins at FPSAC 2018 | extended abstract (12 pages)

• Zamolodchikov periodicity and integrability
  An extended abstract prepared for FPSAC 2017 | extended abstract (12 pages)

• Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions
  A talk given by Gaku Liu at FPSAC 2016 | slides (25min) | extended abstract (12 pages)

• Weak separation, pure domains and cluster distance
  A poster presented by me at FPSAC 2016 | pdf (poster) | extended abstract (12 pages)