Windows and Geometric Invariant Theory
Explore the theory of windows, a powerful tool for studying derived categories of algebraic varieties in Geometric Invariant Theory (GIT) constructions, in this lecture by Sebastian Torres from the University of Miami/IMSA. Delve into the applications of window theory, including cohomology computations and semi-orthogonal decompositions. Examine how this relatively recent theory, introduced by Halpern-Leistner and Ballard, Favero, and Katzarkov, provides insights into the behavior of derived categories during wall crossings as stability conditions vary. Cover key topics such as standard flips, transformations, semistable lockers, equivalence classes, and variations of GIT, gaining a deeper understanding of this important area in algebraic geometry.