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Hessenberg varieties are sub-varieties of a full flag variety which arise in many areas of mathematics, including geometric representation theory, numerical analysis, mathematical physics, combinatorics, and algebraic geometry. Special families of Hessenberg varieties include Springer varieties (which play a fundamental role in geometric representation theory), Peterson varieties (which arise when we study the quantum cohomology of flag varieties), and the toric varieties associated with Weyl chambers (which provides a connection between root systems and toric varieties).

Exciting recent developments in this area include: (1) new connections with graph theory, in connection with a conjecture of Stanley and Stembridge, (2) the theory of "generalized splines" being pioneered by Tymoczko and collaborators, used to study questions related to Hessenberg varieties and Schubert calculus, and (3) the link to the theory of Newton-Okounkov bodies, and their associated integrable systems. This workshop will provide researchers an informal setting in which to exchange ideas and formulate open questions at the forefront of the study of Hessenberg varieties.