Instructor: Antonio Villanacci
The course is an independent study on topics in mathematical economics. The course “Mathematics for economics” is a prerequisite. The content of the exam has to be discussed and agreed upon with the instructor. Possible topics are listed below.
1. General topology.
2. Measure theory.
3. Banach Spaces and Calculus in Banach Spaces.
4. Linear system of Differential Equations.
5. Nonlinear systems of differential equations.
6. Convex Analysis.
7. Differential Topology.
8. Dynamic Programming.
9. Functional Analysis
10. Contract Theory, Mechanism Design, Auction Theory. (Professor Domenico Menicucci)
11. Discrete Mathematics and Social Choice Theory (Professor Michele Gori)
12. Topics in order theory and its applications to microeconomics and industrial economics (Professor Federico Quartieri)
13. Financial risk measures and their dual representations (Professor Giacomo Scandolo)
For each topic, notes from the instructor are the main required reading for the course and are available upon request (by email), and a textbook is suggested as optional readings. The exam will based on a written paper by the student and/or some meetings in which the student will talk about the content of the notes.