Department of Mathematics
"Affine Linking Numbers and the Causality Relation for Wave Fronts"
based on the joint papers with
Yu. Rudyak from the University of Florida Gainesville.
Vladimir Chernov
Dartmouth College
The linking number is the classical invariant of the pair knots which is the number of intersections of one knot with a surface bounded by the other. We construct affine linking numbers that are extensions of linking numbers to the case where knots in question do not bound any surface. A CR causality invariant of the pair of fronts of two events is the algebraic number of times the earlier front has passed through the origin of the later front before the later front appeared, and it measures how strongly the earlier front influenced the event that caused the second front. We show that affine linking numbers can be effectively used to calculate the CR causality relation invariant from the current picture of the fronts of two signals without any knowledge of the signal propagation law. We also use it to count the algebraic number of times a front passed though a marked point between the two time moments.
All interested persons are welcome.
The talk will be accessible to upper class students.