[Binghamton Geometry/Topology Seminar] (no subject)

[Ross Geoghegan]

                   BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Thursday October 12, 2006

   Time:  2.50 pm

   Place: Library North 2205 followed by coffee/tea in the Anderson
          Reading Room.

   Speaker: Paul Loya (Binghamton) 

   Title: Elementary complex analysis made a little complicated: The
          Cauchy integral and transform on regions with corners

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 transform, which (roughly speaking) is just
the Cauchy integral restricted to the contour. This transform has some
amazing properties we'll talk about.


NOTE:  The seminar has a webpage where the semester's program is listed:

http://math.binghamton.edu/MATH/dept/topsem/index.html

It can also be linked from the Department's Home Page.
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