APMA 2811G- Topics in Averaging and Metastability with Applications

Instructor: Konstantinos Spiliopoulos

Office: 37 Manning St, room 101
Office Hours: By appoitment
Email: kspiliop_at_dam.brown.edu
to send me an email replace _at_ by @.
Meets: Thursdays 10:30-1:00 at 180 George St room 102A
Organizational meeting: Wednesday, Sep 1st, 11-12 noon, 182 George Street, Room 110.

Recommended textbooks:

Syllabus (pdf)

Course Description: Metastability and stochastic resonance phenomena appear every often in various scientific disciplines. Typical examples include the dynamical behavior of proteins, magnetic systems with magnetization opposite to the external field, etc. Roughly speaking, metastability refers to the phenomenon of rare transitions of a system between different stable equilibriums. Even though these transitions are rare, they usually have very important effects on the behavior of the system. A closely related phenomenon is stochastic resonance. Stochastic resonance occurs when a multistable system, subject to noise, displays an organized behavior which is different from its behavior in the absence of noise. Therefore, establishing a mathematical theory of metastability is extremely important for applications. One of the main tools in the mathematical theory of metastability is large deviations theory. The construction of a mathematical theory of metastability not only provides interesting and physically relevant applications of the already established large deviation theory, but also poses new problems.

Emphasis will be placed on

The course material will be based on theory, methods and examples from various scientific disciplines.

The course will focus on metastability and use the theory of large deviations as a tool, rather than developing the theory of large deviations.