Talk page
Title:
Amoebas, Ronkin function and Monge-Amp\`er measures of algebraic curves with marked points
Speaker:
Abstract:
Algebraic curves with a pair of real normalized differentials are central for many aspects of the algebraic-geometrical integration theory. They provide a unifying framework for the Hamiltonian theory of soliton equations, the Whitham equations, WDVV equations, Siberg-Witten solution of $N=2$ SUSY gauge models. Recently, they found new applications to the study of geometry of moduli spaces of curves with punctures. In the talk new constructions and notions associated with algebraic curves with a pair of real normalized differentials will be introduced. They generalize concepts of amoebas, Ronkin functions associated with plane curves. The later have played crucial role in the recent progress in the theory of real algebraic curves (Mikhalkin) and in the theory of limiting shapes of random surfaces (Kenyon, Okounkov, Sheffield).
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