Enumerative geometry is a classical branch of complex algebraic geometry dedicated to counting geometric configurations in an algebraic variety. For example, the Gromov-Witten and Donaldson-Thomas invariants respectively count curves and coherent bundles in a complex algebraic variety.
This lecture will focus on recent advances in enumerative geometry, in two different directions. The first part will be devoted to general results on Gromov-Witten invariants, valid for varieties of arbitrary dimension and related to the geometry of moduli spaces of stable curves. In the second part, specific results for dimensions two and three will be presented, combining Gromov-Witten invariants, Donaldson-Thomas invariants, tropical geometry and modular forms.
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Guest lecturer
Recent advances in enumerative geometry
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