Riemann surfaces and their applications in integrable system
Teaching & Academics
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In this course we discuss very interesting and beautiful object - Riemann surfaces. Riemann surfaces have many different applications in integrable systems. And one of our main aim is to explain how Riemann surfaces and their degenerations in singular algebraic curves help to solve problems from geometry and integrable models of mathematical physics. For example, one of such models is a famous Korteweg-de Vries equation:
ut = (6 u uxx +uxxx )/4, u = u(x, t).
This equation describes solitons, that is, solitary water waves in a channel.