Amplituhedra and Total Positivity (AToP) Workshop
Amplituhedra and Total Positivity (AToP) Workshop
UC Davis, August 3-6 2026
UC Davis, August 3-6 2026
This workshop is aimed at (particularly early-career) researchers interested in working on combinatorial and geometric problems related to the amplituhedron, positive geometries, and other generalizations of total positivity.
Dates: August 3-6
Location: Mathematical Sciences Building, UC Davis.
Format: A small number of talks in the mornings, focused on exposing participants to relevant background, recent advances in the field, and useful techniques for research. Afternoons will be spent working in small groups on open problems.
Registration: If you are interested in participating, please fill out the application form no later than April 22. Applications from researchers who have no prior experience with the amplituhedron but are familiar with topics in total positivity (e.g. one or more of the totally nonnegative Grassmannian, cluster algebras, positroid varieties) are welcome.
Funding: We anticipate being able to fully cover accommodation for participants. There is some funding available for domestic travel as well; exact amounts will be communicated after the application deadline.
If you have questions: Contact Melissa Sherman-Bennett (lead organizer) at mshermanbennett "at" ucdavis.edu.
Travel by plane: The closest and most convenient airport is Sacramento (SMF), which is about 25 minutes away from Davis by car or 45 minutes by the bus (Yolo bus 42B from the airport to Davis, 42A from Davis to the airport, round-trip fare is around $3). Other, much further airports are SFO and OAK, both about 1.5 hours from Davis by car and 2.5-3 hours by public transit (BART + Amtrak, round-trip cost around $75). Usually it is not worth it to fly to SFO, given the time and expense to travel from SFO to Davis.
Travel by train: Amtrak Capitol Corridor runs from San Jose to Sacramento and stops in Davis.
Hotels: Best Western University Lodge and Aggie Inn are located halfway between campus and downtown. Another (usually more expensive) option very close to campus is Hyatt Place. We don't recommend staying in hotels across the I-80 from campus, as they are rather far away from the Mathematical Sciences Building.
Picnic in the park: In the summer, the Davis Farmer's Market runs Wednesdays from 4-8pm, with live music.
TBA
If you would like to learn about the amplituhedron before the workshop,
The positive Grassmannian, amplituhedra, and clusters (Williams) is an excellent survey article.
Here are notes and videos from a 4-lecture series I gave on the amplituhedron: lectures I, II, III, IV
Some research papers which could be possible references for a morning talk. By no means an exhaustive list!
m=1
The m=1 amplituhedron and cyclic hyperplane arrangements (Karp, Williams)
m=2
The positive tropical Grassmannian, the hypersimplex and the m=2 amplituhedron (Lukowski, Parisi, Williams)
The m=2 amplituhedron and the hypersimplex (Parisi, Sherman-Bennett, Williams)
m=4
The amplituhedron BCFW triangulation (Even-Zohar, Lakrec, Tessler)
BCFW tilings and cluster adjacency for the amplituhedron (Even-Zohar, Lakrec, Parisi, Sherman-Bennett, Tessler, Williams)
Amplituhedra and origami (Galashin)
General m
Parity duality for the amplituhedron (Galashin, Lam)