During his Center appointment, Professor Yong will prepare a monograph about the Grassmannian, a classical and fundamental geometric object appearing in mathematics, science, and engineering.
The Grassmannian is defined as the parameter space of all linear subspaces of fixed dimension in n-dimensional space. Collectively, combinatorial theorems about the Grassmannian have recently crystallized into a state of substantial beauty and simplicity. This has opened the door to new creative and foundational work in the classical setting, through finding new relationships between disparate ideas.Professor Yong will research topics that affect three fields: combinatorics (analysis of discrete structures), algebraic geometry (theory of systems of polynomial equations), and representation theory (algebra of symmetries). He will guide Illinois student and postdoc researchers in the use of modern computation to seek conjectures and theorems. He plans to invite guest speakers to the Algebra-Geometry-Combinatorics seminar, to enrich local training in these areas. He will also travel to several research universities to consult with leading experts.