TGTS Tetrahedral Geometry/Topology Seminar

Sponsored by Elizabethtown College, Franklin and Marshall College,
Lebanon Valley College, and Millersville University

Speakers 2015-2016

11 September  Mahmoud Zeinalian, Long Island University
 2 October    James Hughes, Elizabethtown College
 6 November   David Futer, Temple University
 4 December   Barbara  Nimershiem, Franklin and Marshall College, 
              Ron Umble, Millersville University, and
              Merv Fansler, Millersvill University
 5 February   Terrance Napier, Lehigh University
 4 March      Thomas Hunter, Swarthmore College     
 1 April      David Lyons, Lebanon Valley College
TGTS is a regional mathematics seminar/colloquium. We meet at 4:30 p.m. on the first Friday of each month during the academic year (with some exceptions, as noted in the schedule above). The public is cordially invited to attend.

Next Talk

    Date: 5 February 2016, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Terrance Napier, Lehigh University
   Title: The Bochner-Hartogs dichotomy

Abstract. In 1906, Friedrich Hartogs discovered that holomorphic
(i.e., complex analytic) functions in several complex variables have the
following extension property.  Let K be a compact set with connected
complement E in complex Euclidean space C^n of dimension n>1, and let f
be a holomorphic function on E.  Then there exists a unique holomorphic
function g on all of C^n such that the restriction of g to E is equal to
f. Clearly, this fails in dimension n=1 (take f(z)=1/z for example).  Of
course, it had long been known that in one variable, the geometry and
topology of a domain (or more generally speaking, a Riemann surface)
have strong implications for complex analysis on the domain. Hartogs’
discovery was probably the first indication of the ways in which
geometry and topology, in the form of convexity and the ends structure,
might enter in higher dimensions.  This theme played a central role in
the development of the theory of several complex variables.

One may view this Hartogs property as the vanishing of the first
compactly supported cohomology with coefficients in the structure sheaf.
We will consider analogues for certain complete Kaehler manifolds.  More
precisely, we will look at conditions under which a connected noncompact
complete Kaehler manifold X satisfies the Bochner-Hartogs dichotomy:
Either the first compactly supported cohomology of X with coefficients
in the structure sheaf vanishes, or X admits a proper holomorphic
mapping onto a Riemann surface.

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