To take part, please, on June 26 after 3:45 pm Novosibirsk time (UTC+7) connect to the Zoom conference via this link: https://zoom.com.cn/j/66634384173?pwd=UXhTZVBwMDNBVnU1Vk4vSGR0aW1jdz09.
Quot-schemes of Grassmannian type naturally arise as resolutions of degeneracy loci of maps between vector bundles over a scheme. In this talk we will discuss the relationships of the derived categories and Chow groups among these Quot-Schemes. This provides a unified way to understand many known formulae such as blowup formula, Cayley's trick, projectivization formula, Grassmannian bundles formula and formula for Grassmannain type flops and flips, as well as provide new phenomena such as virtual flips. We will also discuss applications to the study of moduli of linear series on curves, blowup of determinantal ideals, generalized nested Hilbert schemes of points on surfaces, and Brill-Noether problem for moduli of stable objects in K3 categories.