Amplituhedra and Total Positivity (AToP) Workshop

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, 2026
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: Registration is now closed.

Funding: We will cover accommodation for all participants. There is some funding available for travel as well; exact amounts will be communicated by email.

If you have questions: Contact Melissa Sherman-Bennett (lead organizer) at mshermanbennett "at" ucdavis.edu.

Schedule

All talks will be in MSB 2112. Working groups can use MSB 2112, 2240, 3240, and 3106.

Some references

If you need to brush up on total positivity and the totally nonnegative Grassmannian:

• The totally nonnegative Grassmannian and Grassmann polytopes (Lam)
• Notes from a topics course on total positivity at Davis

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!

• The m=1 amplituhedron and cyclic hyperplane arrangements (Karp, Williams)
• 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)
• 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)
• Parity duality for the amplituhedron (Galashin, Lam)
• Amplituhedron cells and Stanley symmetric functions (Lam)

Participants

• Evgeniya Akhmedova, University of Michigan
• Penelope Beall, UC Davis
• Jonah Berggren, University of Kentucky
• Timothy Blanton, UC Davis
• Jonathan Boretsky, McGill/LACIM
• Amanda Burcroff, MIT
• Joao Pedro Carvalho, University of Michigan
• Ariana Chin, UCLA
• Colin Defant, Harvard University
• Yassine El Maazouz, Caltech
• Moriah Elkin, Cornell University
• Chaim Even-Zohar, Technion, Haifa
• Eugene Gorsky, UC Davis
• Yuhan Jiang, UC Berkeley
• Soyeon Kim, UC Davis
• Rajbir Longia, University of Waterloo
• Paul Mammen, University of Michigan
• Yelena Mandelshtam, University of Michigan
• Thomas Martinez, UCLA
• Michael Oren Perlstein, Weizmann Institute of Science
• Timothy Paczynski, UC Davis
• Matteo Parisi, Okinawa Institute of Science and Technology
• Daniel Qin, UC Davis
• Amanda Schwartz, UC Davis
• Dawei Shen, University of Michigan
• Melissa Sherman-Bennett, UC Davis
• Ran Tessler, Weizmann Institute of Science
• Matthew Tyler, UCLA
• Chenglu Wang, Harvard University
• Bailee Zacovic, University of Michigan

Information about Davis

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 and are walking distance from the Mathematical Sciences Building. Another (usually more expensive) option very close to campus is Hyatt Place. The other hotels downtown are also walking distance to MSB. The hotels across the I-80 from campus are often cheaper, but are not easily walkable from campus, so if you stay there you may need to take the bus (fairly infrequent).

Picnic in the park: In the summer, the Davis Farmer's Market runs Wednesdays from 4-8pm, with live music.

My research is supported by the NSF under Award No. 2444020.