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Institute for Advanced Study in Mathematics (IASM)

The theories of rational/trigonometric/elliptic functions were developed as functions over plane/cylinder/torus, respectively, before the 20th century. Among them, the theory of elliptic functions is most interesting, and it can be understood as the parent theory of the rest. During the 20th century, the same rational/trigonometric/elliptic trichotomy has been also found in integrable systems, algebras and cohomology groups. Like the theory of functions, recent development reveals that the relationship among integrable system, algebra, geometry, and physics becomes most profound at elliptic level. In particular, Lie algebras (rational) are promoted to affine Lie algebras (trigonometric) and toroidal Lie algebras (elliptic). The workshop aims at investigating quantum versions of toroidal Lie algebras, called quantum toroidal algebras.

Physique mathématique,    Géométrie et topologie

Institute for Advanced Study in Mathematics (IASM)

This workshop will tackle some fundamental open questions about Artin-Schelter regular algebras, in particular, elliptic algebras, and their associated Poisson structures. In particular, it will focus on the correspondence between the representations of elliptic algebras and the symplectic leaves of their semi-classical limits, as well as on the relationship between the deformation theory of Artin-Schelter regular algebras and that of the derived category or the A-infinity-category of related projective schemes. This workshop brings together leading experts in algebra and geometry from around the world to identify and attack these outstanding problems and to collaborate for future breakthroughs.