Abstract: The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts that reflect a certain range of developments, but even in their totality they cannot be taken as a comprehensive survey. In the format of a 30-page contribution aimed at a general mathematical audience, I have decided to illustrate some of the basic ideas in one very interesting example – that of Hilb(C^2, n), hoping to spark the curiosity of colleagues in those numerous fields of study where one should expect applications.
https://eta.impa.br/dl/PL003.pdf
https://arxiv.org/abs/1801.09818
本文通过具体的例子：复平面C^2上n个点的Hilbert概型Hilb(C^2, n)及其类比：三维簇的Donaldson-Thomas理论,引入丰富的结构：计数代数几何，几何表示论, 中岛的箭簇(quiver varieties)，量子可积系统，量子群的几何作用，K-理论，单值化和导出等价。
相关附件
4-PL003 Okounkov.pdf
