Integral geometric regularity

Analysis Seminar
Wednesday, October 31, 2018 - 1:55pm for 1 hour (actually 50 minutes)
Skiles 005
Joe Fu – UGA – johogufu@gmail.com
Galyna Livshyts
The centerpiece of the subject of integral geometry, as conceived originally by Blaschke in the 1930s, is the principal kinematic formula (PKF). In rough terms, this expresses the average Euler characteristic of two objects A, B in general position in Euclidean space in terms of their individual curvature integrals. One of the interesting features of the PKF is that it makes sense even if A and B are not smooth enough to admit curvatures in the classical sense. I will describe the state of our understanding of the regularity needed to make it all work, and state some conjectures that would extend it.