Elliptic Algebra and Characteristic Classes of Link Patterns

Explore a mathematical seminar lecture examining the relationships between three geometric object families: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of square-zero matrices. Delve into how these families are respectively governed by permutations, partial permutations, and 'link patterns'. Learn about the equivariant elliptic cohomology characteristic classes of these geometric objects, developed using the Borisov and Libgober framework, and how they satisfy Okounkov's stable envelope axioms. Discover the application of Hecke-type algebra in computing elliptic classes and its extended action across permutations and link patterns, leading to enhanced understanding of duality. Delivered by Professor Andrzej Weber from the University of Warsaw as part of the New equivariant methods in algebraic and differential geometry (EMG) series at the Isaac Newton Institute.