Mathematics Colloquia and Seminars

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The Deligne-Mumford moduli space M_{g,n} of marked stable curves of genus g has been the subject of a large body of work, however, its intersection theory is far from being completely understood. Most recent work has been focused on describing the so-called tautological ring of M_{g,n}, defined by a natural collection of classes in the Chow or cohomology rings. Recently, two large collections of tautological relations were found, both conjectured by Pixton: the 3-spin relations, proved by Janda, Pandharipande, Pixton and Zvonkine, and the double ramification relations, proved by Clader and Janda. I will show how these relations can be used to effectively find boundary formulas for tautological classes of sufficiently high codimension. This is joint work with Clader, Grushevsky, Janda and Wang.