The Betti numbers of moduli spaces of genus 0 stable maps

Massimo Bagnarol
Wednesday, May 2, 2018 - 16:15

Since their introduction by Kontsevich in 1995, stable maps and their moduli have revealed to be increasingly important both in mathematics and in physics, because of their applications in various fields (enumerative geometry, symplectic topology, string theory, etc). This talk will be devoted to the study of the cohomology of moduli spaces of genus 0 stable maps into a smooth projective variety X. The case where X is a complex projective space was studied by Getzler and Pandharipande, using the combinatorial properties of these spaces. We will show that their method can be adapted to consider the more general case where X is a complex Grassmannian. This is joint work in progress with Fabio Perroni. In the spirit of GMPS seminars, we will focus more on ideas and motivations rather than technicalities.

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