Analysis Seminar

I will discuss some recent work with J. Gong on large classes of "fat'' carpets that possess Poincare inequalities. These generalize the examples of Tyson, Mackay and Wildrick. I will also discuss some related ideas and questions on "thin'' carpets, such as the standard Sierpinski carpet. In addition to designing beautiful carpets for your living room, perhaps this talk also will give a sense of how natural objects carpets are and how they arise in different areas of geometry and topology.