ICTS:30022

Video URL

ICTS colloquium - Integrable combinatorics

ICTS colloquium - Integrable combinatorics

(2024). ICTS colloquium - Integrable combinatorics. SciVideos. https://youtube.com/live/znYSGh1HMeE

ICTS colloquium - Integrable combinatorics. SciVideos, Oct. 21, 2024, https://youtube.com/live/znYSGh1HMeE 

          @misc{ scivideos_ICTS:30022,
            doi = {},
            url = {https://youtube.com/live/znYSGh1HMeE},
            author = {},
            keywords = {},
            language = {en},
            title = {ICTS colloquium - Integrable combinatorics},
            publisher = {},
            year = {2024},
            month = {oct},
            note = {ICTS:30022 see, \url{https://scivideos.org/icts-tifr/30022}}
          }
Philippe Di Francesco
Talk numberICTS:30022
Source RepositoryICTS-TIFR
Source EventDiscrete integrable systems: difference equations, cluster algebras and probabi…
Collection

Abstract

Combinatorics has constantly evolved from the mere counting of classes of objects to the study of their underlying algebraic or analytic properties, such as symmetries or deformations. This was fostered by interactions with in particular statistical physics, where the objects in the class form a statistical ensemble, where each realization comes with some probability. Integrable systems form a special subclass: that of systems with sufficiently many symmetries to be amenable to exact solutions. In this talk, we explore various basic combinatorial problems involving discrete surfaces, dimer models of cluster algebra, or two-dimensional vertex models, whose (discrete or continuum) integrability manifests itself in different manners: commuting operators, conservation laws, flat connections, quantum Yang-Baxter equation, etc. All lead to often simple and beautiful exact solutions.