Instructor: Andrea Bertozzi
This course will cover some advanced topics in nonlinear partial differential equations, with applications to image processing and aggregation phenomena. The syllabus will be broken up by the type of phenomena of interest. Students will attend lectures, read current and recent literature, and do projects on current research topics. This course is specially designed for students to work on a miniproject connected with the course that could result in a refereed journal publication. Students getting credit for the course will be assigned a research problem near the beginning of the course and will do additional reading related to that problem. They will be expected to do an in class presentation on that problem at some point during the course, as well as to write a paper about the problem. Students who take this course should have a minimum of the 266 or 269 sequence, preferably both. The course is designed for those who have passed the ADE qual and the Numerical qual, although it is possible to take the course with only one qual.
Part I: Finite time singularities in nonlinear PDE.
This part of the course will cover finite time singularities in nonlinear PDE. Suggested reading:
Part II: Pattern formation - aggregation phenomena, diffuse interfaces, and coarsening.
Course schedule: The course will meet NMF from 1-2pm.