University of Connecticut

Course Info

MATH 5016: Topics in Probability

Description: Advanced topics in probability theory, theory of random processes, mathematical statistics, and related fields. With a change of content, this course is repeatable to a maximum of twelve credits.

Credits: 3

MATH 5016 - Section 1: Topics in Probability

Description: The course will cover the following topics:

  1. Subelliptic diffusion operators
  2. Subelliptic diffusion semigroups
  3. Diffusion processes
  4. The heat semigroup on a Riemannian manifold
  5. Brownian motion on a Riemannian manifold
  6. Ricci curvature and stochastic completeness
  7. Functional inequalities under Ricci curvature lower bounds
  8. Coupling by parallel transport and reflection with applications
  9. An Introduction to the stochastic approach to index theory: The Gauss-Bonnet-Chern theorem
  10. An Introduction to  analysis on curved path spaces
  11. An introduction to the stochastic analysis of foliated manifolds
Lecture notes will be posted on my blog

Offered: Fall

Credits: 3

Sections: Fall 2016 on Storrs Campus

PSCourseID Course Sec Comp Time Room Instructor
14511 5016 001 Lecture TuTh 12:30:00 PM-01:45:00 PM MONT 314 Baudoin, Fabrice