Abstracts
Andrew Harder (Miami) – Hodge numbers of Landau-Ginzburg Models Katzarkov, Kontsevich and Pantev define two sets of invariants of Landau-Ginzburg models which play the role Hodge numbers in the usual mirror symmetry story. I will discuss these numbers, their relation, computation, and how they can be used to deduce Hodge-theoretic restrictions on the Landau-Ginzburg mirrors to Fano manifolds. This is based on joint work with Katzarkov, Lunts and Przyjalkowski. Caucher Birkar (Cambridge) – Altering FibrationsIn this talk I will discuss singularities on fibrations. In particular, we focus on bounded families over curves and try to explain how one may alter the fibration to make the singularities of the fibres as simple as possible but keeping the boundedness condition. Jesus Martinez Garcia (Bath) – K-Stability, Canonical Metrics, and Calabi Dream Rational SurfacesThe search for metrics which are “canonical” goes back to Calabi’s work in the 50s. Progress in recent decades has related the existence of Kaehler metrics with constant scalar curvature to the algebraic-geometric notion of K-stability, culminating in the Yau-Tian-Donaldson conjecture. In this talk we will introduce these notions and focus on the study of K-stability on polarised rational surfaces. We will introduce natural questions and offer some partial answers. In particular, we will use birational geometry to classify all Calabi dream rational surfaces. These surfaces, introduced by Chen and Cheng, are those admitting a constant scalar curvature Kaehler metric in each Kaehler class.
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