Àííîòàöèÿ:
In the 1970s, a method was devised to use Jacobians of algebraic curves and the corresponding theta functions to write out exact solutions to some well-known equations of mathematical physics, namely those obtained from the Kadomtsev–Petviashvili hierarchy (an infinite system of partial differential equations), in particular, the Korteweg–de Vries and Kadomtsev–Petviashvili equations. These solutions are based on the geometry of algebraic curves and line bundles on them (or, more generally, torsion-free sheaves), rings of commuting ordinary differential operators, and the Krichever map, which associates certain algebraic-geometric data associated with a projective curve and a line bundle on it with a point in an infinite-dimensional algebraic variety, the Sato Grassmannian. This correspondence (known as the Krichever correspondence) was subsequently refined and developed by many renowned mathematicians (W. Drinfeld, D. Mumford, J. Verdier, G. Segal, D. Wilson, M. Mulase, T. Shiota), and played an important role in solving the Schottky problem.
In my talk I will attempt to outline the basic definitions and constructions of this theory.
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Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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