The contents of the course change depending on the knowledge and the interests of students. The following is a list of topics studied in the last editions of the course, only a part of this will be covered.
·Lie Groups ·The method of characteristics ·The geometrical meaning of a differential equation ·Symmetry and reduction of a differential equation ·Symmetry in variational problems ·Lax systems ·Integrable systems ·Vector fields and forms ·Differential equations in Pfaff form ·Symmetry of differential equations in the Pfaff formalism ·Frobenius theorem for vector fields ·Frobenius theorem for forms ·Gauge theories and the Higgs mechanism
Prerequisites for admission
It will be assumed the student knows the material covered in the B.Sc. ("Laurea Triennale") program
The following material refers to the first part of the course; additional material will be indicated depending on the actual program covered.
P.J. Olver, Application of Lie groups to differential equations, Springer 1986 P.J. Olver, Equivalence, invariants, and symmetry, Cambridge 1995 H. Stephani, Differential equations, Cambridge 1989
Some lecture notes will also be available
Assessment methods and Criteria
The exam will be an oral one, the exact format will be communicated later on and will depend on the sanitary (COVID-related) situation. It will aim at evaluating the student's knowledge and comprehension of the arguments covered as well as the capacity to apply them.