Link to the
Analysis MATH 742, Fall 2016
- Lectures : Tuesday-Thursday 9:30-10:45pm, MATH 0403.
- Instructor : Pierre-Emmanuel Jabin
- Contact information, Phone : 301 405 5122, Office : 2307
in Math. Bldg and 4149 in CSCAMM, e-mail : firstname.lastname@example.org
- Office hours: Tuesday-Thursday 2PM-3PM
- Textbook: There is no required
textbook but the class will use materials from Optimal Transport, Old
and new, by C. Villani (ISBN 978-3-540-71050-9) and Gradient Flows in
metric space and in the space of probability measures, by L. Ambrosio,
N. Gigli and G. Savare (ISBN-13:
- Material: A more complete description of the material covered week by
week and assignmnents can be found at the address http://www2.cscamm.umd.edu/~jabin/Schedule16_742.html
- Homework: There will be several individual
projects to be completed.
- Grade: The grade will based on the projects.
- Disabilities : Please inform me as soon as possible if you need
accommodations because of a disability.
- Communication : Information about the course will be given during
class and through this web page. In specific cases (unexpected class
cancellations), students will be contacted by e-mail.
- Academic integrity : The University of Maryland, College Park has a
nationally recognized Code of Academic Integrity, administered by the
Student Honor Council. This Code sets standards for academic integrity
at Maryland for all undergraduate and graduate students. As a student
you are responsible for upholding these standards for this course. It is
very important for you to be aware of the consequences of cheating,
fabrication, facilitation, and plagiarism. For more information on the
Code of Academic Integrity or the Student Honor Council, please visit www.shc.umd.edu. To further exhibit
your commitment to academic integrity, remember to sign the Honor Pledge
on all examinations and assignments: "I pledge on my honor that I have
not given or received any unauthorized assistance on this examination
- Some examples about academic integrity : It is all right for students
to discuss between them about the projects. It is similarly permitted to
look for tips on the internet,
from other students or other resources. It is wrong to simply copy from
any student, a book, a web page or any other source.
Course Description (Preliminary)
This class introduces some basic notions of analysis
and calculus of variation in the context of Riemannian geometry. In
particular some of the goals of the class are
- Understand the basic concepts around solving Partial Differential
Equations in a non-Euclidian setting.
- Understand the basic theory of gradient flows on
a Riemannian or pseudo-Riemannian manifold.
- Define the necessary pseudo-Riemannian structure
on the space of probability measures.
- Model and study parabolic equations on a manifold
using gradient flows and understand their connection to basic
- Consider some elementary flows in infinite
dimension, such as the limit of a Brownian motion when the dimension
goes to infinity.
No priori knowledge of stochastic analysis is required for this class,
only basic notions of calculus of variation, differential geometry and