• Brian Harbourne (BH): Seshadri constants, Waldschmidt constants and resurgences.
    Abstract: Recent work on ideal containments has led to the development of the concept of the resurgence, a new asymptotic invariant of ideals, which in turn has led to renewed interest in a quantity introduced in the late 1970s by Waldschmidt, now called Waldchmidt constants, which have connections to other asymptotic invariants such as Seshadri constants (introduced in the 1990s by Demailly), to resurgences (introduced by Bocci-Harbourne in 2000s) and Harbourne constants (growing out of a workshop at Oberwolfach in 2010). Harbourne's lectures for this school will cover aspects of all three of these invariants, their relationships, and some of their applications in Algebraic Geometry and Commutative Algebra. Notes (updated on April 6, 2017)

  • T. R. Ramadas (TR): Divisors and line bundles, and maps to projective spaces, Intersection theory on surfaces, Riemann-Roch for surfaces, Nakai, Kleiman, and Seshadri criteria for ampleness. Notes

  • Krishna Hanumanthu (KH): Cohomology of coherent sheaves, cohomology of line bundles on projective space. Seshadri constants, Waldschmit constants. Bounds on Seshadri constants. Notes

  • D. S. Nagaraj (DSN): Riemann-Roch for curves, blow-ups of surfaces.

  • Manoj Kummini (MK): Serre duality. Notes

  • M. S. Narasimhan (MSN): Birational Geometry.

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