Young-Hoon Kiem：Representations on the cohomology of the moduli spaces of pointed stable curves of genus 0
Abstract: The moduli spaces of pointed stable curves have played a major role in enumerative algebraic geometry. Much is known about their cohomology but we still don't have a complete understanding of the symmetric group actions by permuting the marked points. I will talk about a new construction of the moduli spaces of pointed stable curves of genus 0, by an investigation on wall crossings of moduli spaces of quasimaps, which was motivated by the Landau-Ginzburg/Calabi-Yau correspondence. Using this construction, we give a closed formula for the characters of the symmetric group actions on the cohomology. Motivated by Manin and Orlov's question about the existence of an equivariant full exceptional sequece in the derived category of the moduli spaces, it is natural to ask if the cohomology groups are permutation representations or not. Using our closed formula, we provide partial answers to this question. Based on a joint work - arXiv:2203.05883 - with Jinwon Choi and Donggun Lee.