Title: Analysis and geometry in Carnot groups
Speaker: Scott Zimmerman
Abstract: Carnot groups are particularly nice Lie groups, and these manifolds provide mathematical models for scenarios in which motion is controlled by predefined constraints. Such restrictions endow a Carnot group with a non-smooth structure and unusual geometric properties. This unconventional framework requires the development of new and creative solutions to questions of classical analysis.
In this talk, I’ll define Carnot groups and introduce the sub-Riemannian Heisenberg group. This Lie group is the simplest non-trivial example of a Carnot group, and I’ll explain the relationship between the geometry of the group and some questions of analysis on it. After this introduction, I will discuss in more detail some work that I have done on the smooth extendability of curves in the Heisenberg group as well as more recent research into the boundedness of singular integral operators defined along Carnot curves.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn Semester. Pre-candidacy PhD students can sign up for this lecture series by registering for two credit hours of Math 6193 with Professor Nimish Shah.
