Open Problems in Algebraic Combinatorics

Speakers:

• Sami Assaf
• Sylvie Corteel
• Philippe Di Francesco
• Sergey Fomin
• Pavel Galashin
• Eugene Gorsky
• June Huh
• Joel Kamnitzer
• Rick Kenyon
• Allen Knutson
• Thomas Lam
• Anton Mellit
• Igor Pak
• Greta Panova
• Alex Postnikov
• Claudiu Raicu
• Steven Sam
• Ralf Schiffler
• Anne Schilling
• David Speyer
• Hugh Thomas
• Julianna Tymoczko
• Lauren Williams
• Nathan Williams

In light of the postponement of the conference, more info about funding will be posted at a later date.

In light of the postponement of the conference, more info about registration and travel will be posted at a later date.

Tentative talk titles:

• Sami Assaf: Using polynomials to resolve open problems in representation theory and geometry
• Sylvie Corteel: Cylindric partitions
• Philippe Di Francesco: The combinatorics of triangular ice
• Eugene Gorsky: Generalized q,t-Catalan polynomials and link invariants
• June Huh: Lorentzian polynomials
• Joel Kamnitzer: Canonical bases in representation theory and cluster algebras
• Rick Kenyon: Dimers and related models
• Thomas Lam: Positive geometries
• Anton Mellit: Combinatorial expressions for the nabla operator
• Igor Pak: Complexity aspects and challenges in algebraic combinatorics
• Greta Panova: Structure constants in algebraic combinatorics: from Geometric Complexity Theory to Asymptotics
• Claudiu Raicu: Homological invariants of $S_n$-equivariant monomial ideals
• Steven Sam: Combinatorial problems inspired by representation stability
• Ralf Schiffler: Perfect matching problems in cluster algebras and number theory
• Anne Schilling: How crystals might help to make progress on plethysm coefficients

The conference will be accompanied by a proceedings to be published by the AMS. More info about the proceedings to come. Some of the articles for the proceedings are already available online here:

• A positivity conjecture on the structure constants of shifted Jack functions by P. Alexandersson and V. Féray
• The bosonic-fermionic diagonal coinvariant modules conjecture by F. Bergeron
• $(\mathrm{GL}_k \times \mathbb{S}_n)$-modules of multivariate diagonal harmonics by F. Bergeron
• Order polynomial product formulas and poset dynamics by S. Hopkins
• Increasing subsequences and Kroenecker coefficients by J. Novak and B. Rhoades

An Open Problems in Algebraic Combinatorics blog, to accompany the OPAC 2022 conference and continue afterward, is running online here. A pdf version of the blog posts is also available here.