Miércoles 23 de abril, 15:30 y 17:00, Jacopo Stoppa y Will Donovan, "Twisted cscK metrics..." y "Gromov-Witten invariants...".
Jacopo Stoppa (Imperial College), 15:30.
TITLE: Twisted cscK metrics and Kaehler slope stability.
Abstract: The constant scalar curvature equation on a Kaehler manifold is very different from the Yamabe problem in many respects. For example in the case of projective varieties there are nontrivial cohomological obstructions found by Ross and Thomas. We extend some of these to arbitrary Kaehler manifolds and to a more general equation studied by Fine and Song-Tian. Finally we give some geometric applications via the so-called "adiabatic limit" construction.
Will Donovan (Imperial College), 17:00.
Title: Gromov-Witten invariants for the complex projective plane.
Abstract: How many rational curves of degree d pass through 3d-1 generic points in the complex projective plane? For d=2, we have the result that there is just one conic passing through 5 general points. Beyond this, the question becomes more difficult, and classical enumerative geometry does not provide much hope for a complete solution.
It turns out however that a fairly simple recursion relates the numbers of such curves, allowing them to be calculated. This fact was discovered by Kontsevich in the mid '90s, exploiting the relationship between enumerative geometry and Gromov-Witten invariants.
Without going into any of the analysis underpinning Gromov-Witten invariants, I will explain their relation to enumerative geometry. Then I'll demonstrate some of the axioms of Gromov-Witten theory by describing Kontsevich's calculation in as much detail as time allows.
Miércoles 23 de abril a las 15:30.
Sala de conferencias del Instituto de Óptica Daza de Valdés (c/ Serrano, 121).
TITLE: Twisted cscK metrics and Kaehler slope stability.
Abstract: The constant scalar curvature equation on a Kaehler manifold is very different from the Yamabe problem in many respects. For example in the case of projective varieties there are nontrivial cohomological obstructions found by Ross and Thomas. We extend some of these to arbitrary Kaehler manifolds and to a more general equation studied by Fine and Song-Tian. Finally we give some geometric applications via the so-called "adiabatic limit" construction.
Will Donovan (Imperial College), 17:00.
Title: Gromov-Witten invariants for the complex projective plane.
Abstract: How many rational curves of degree d pass through 3d-1 generic points in the complex projective plane? For d=2, we have the result that there is just one conic passing through 5 general points. Beyond this, the question becomes more difficult, and classical enumerative geometry does not provide much hope for a complete solution.
It turns out however that a fairly simple recursion relates the numbers of such curves, allowing them to be calculated. This fact was discovered by Kontsevich in the mid '90s, exploiting the relationship between enumerative geometry and Gromov-Witten invariants.
Without going into any of the analysis underpinning Gromov-Witten invariants, I will explain their relation to enumerative geometry. Then I'll demonstrate some of the axioms of Gromov-Witten theory by describing Kontsevich's calculation in as much detail as time allows.
Miércoles 23 de abril a las 15:30.
Sala de conferencias del Instituto de Óptica Daza de Valdés (c/ Serrano, 121).
posted by Seminario Junior CSIC at
19:52
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