Abstract: Everyone has used the Cauchy integral in a complex analysis
course. Usually when studying this integral, one considers contours that
are smooth. In my talk I will talk about generalizations of the Cauchy
integral in two ways:
1) When the contour is not smooth but has corners and
2) instead of talking about "analytic functions," which is the main
subject of compex analysis, I'll be talking about "monogenic functions".
The main examples of "monogenic functions" are "harmonic forms" which
can be used to study the topology of manifolds.
We'll also discuss the Cauchy integral, which (roughly speaking) is just
the Cauchy integral restricted to the contour. This transform has some
amazing properties we'll talk about.