Mathematics Colloquia and Seminars

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Moduli spaces of maps from smooth curves to a target variety admit various compactifications. One such compactification is provided by celebrated Gromov compactness theorem and is given by maps from nodal curves (Gromov-Witten theory). For particular types of target varieties, quasimaps, sheaves (Donaldson-Thomas theory) and covers (Hurwitz theory) are three other alternatives. We will discuss wall-crossings between these compactifications on threefolds of the type Surface x Curve. The wall-crossings give rise to interesting correspondences between associated enumerative invariants.