Numbering Code	U-SCI00 44106 LJ55	Year/Term	2022 ・ First semester
Number of Credits	2	Course Type	Lecture
Target Year	4th year students or above	Target Student
Language	Japanese	Day/Period	Wed.2
Instructor name	SHIOTA TAKAHIRO (Graduate School of Science Associate Professor)
Outline and Purpose of the Course	The purpose of the course is to study some aspects of classical integrable systems, including soliton equations. This field was initiated in mathematical physics; nowadays it uses various tools of mathematics, including analysis, representation theory and algebraic geometry. The student who successfully takes this class will become familiar with recent results in soliton theory.
Course Goals	The first goal of the course is to become familiar with the classical results of Soliton Theory (the KP hierarchy, Burchnall-Chaundy-Krichever theory, etc.) and with the tools needed by this theory. The second goal is to become aware of the research trends in Soliton Theory.
Schedule and Contents	We expect to cover the following topics: 1- basic example and preliminary tools: quasiperiodic solutions to the K-dV equation and hyperelliptic curves, line bundles on a Riemann surface (2-3 classes) 2- the KP hierarchy, the 2-D Toda hierarchy and the Burchnall-Chaundy-Krichever theory (3-4 classes) 3- some related integrable systems, including some relatives of the KP and 2-D Toda hierarchies and some finite-dimensional classical integrable systems like Calogero-Moser systems (3-4 classes) 4- characterization of Jacobian and Prym varieties in terms of soliton equations; other topics (4-5 classes) The total number of classes is 15, including feedback.
Course Requirements	A familiarity with calculus, linear algebra, linear ordinary differential equations and complex analysis is necessary.
Study outside of Class (preparation and review)	Students are expected to devote a fair amount of work outside the class to fill in details of some proofs, and prepare reports on side topics.