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Monday, May 13, 2019

**Abstract:** Given an algebraic variety $X$ with an action of a reductive group $G$, geometric invariant theory splits $X$ as the disjoint union $X=X^{ss}\sqcup X^{un}$ of the semistable and unstable locus. The Kirwan-Ness stratification refines $X$ even more by describing $X^{un}$ as a disjoint union of strata $X^{un}=\displaystyle\sqcup_{\beta\in\textsf{KN}} S_\beta$ determined by 1-parameter subgroups $\beta$. In this talk we will describe an algorithm that finds the $\beta$'s and show that such algorithm can be simplified when our space is of the form $T^*V$ where $V$ is a vector space.