Midwest Geometry Conference
May 18 - 20, 2007
to be held in honor of
Thomas P. Branson (1953 -- 2006)

Mathematicians are traveling far to participate in the 2007 Midwest Geometry Conference, and the organizers are fortunate to be able to take advantage of the presence of these distinguished researchers.

We will host 3 Mathematics-AMCS-Physics Colloquia on May 15-16:

Professor A. Rod Gover, University of Auckland, New Zealand  Tuesday, May 15th at 1:30 PM in Lecture Room VAN 301.

Title: Conformal Laplacian operators and Q-curvature on Einstein manifolds. Abstract: Branson's Q curvature is a curvature quantity on even dimensional manifolds which is currently the subject of intense interest from several directions. It's prescription yields a problem which, in terms of elementary geometric analysis,is a higher-dimensional generalisation of the 2-dimensional Gauss curvature prescription problem. On the other hand certain related ``cousin's'' of the Q-curvature yield analogues of the celebrated Yamabe problem. I will sketch the ideas behind a proof that Q and these related quantities are constant on Einstein manifolds. Closely related to these problems is a family of higher order conformal Laplacians due to Graham-Jenne-Mason-Sparling (GJMS) (Paneitz, Reigart, Branson, Wuensch, Eastwood-Singer and others earlier discovered low order cases). I will show that on Einstein manifolds these factor into a composition of second order Laplacian type operators and show that the GJMS family of operators may be extended in this setting. Professor A. Rod Gover is a distinguished researcher, whose research interests include differential geometry, twistor theory and mathematical physics. He is especially focused on a class of differential geometries known as parabolic geometries. This class includes conformal geometries, CR geometries (which turn up in complex analysis), quaternionic geometries, projective differential geometries and many other structures. This colloquium talk is useful as background to some of the MGC talks. It will be given in an audience friendly way and gives some of the background as to why Tom liked Q. A list of his recent preprints and articles is available.

Professor Michael Eastwood, University of Adelaide, South Australia  Tuesday, May 15th at 3:30 PM in Lecture Room VAN 301.

Title: The X-ray Transform on Complex Projective Space. Abstract: The classical Radon transform takes a function on the plane and integrates it over the straight lines in the plane. Its invertibility provides the mathematical basis of modern medical imaging techniques. The X-ray transform takes a function in three-space and integrates it over the straight lines, the terminology being motivated by medical imaging. As one might expect, both of these transforms are best viewed on real projective space. In this talk, I shall discuss what happens on complex projective space where the straight lines are the Fubini-Study geodesics. This is joint work with Hubert Goldschidt. Professor Michael Eastwood is a distinguished researcher. This colloquium talk, as well as his talk tomorrow, is especially geared toward graduate students, and younger researchers, a number of whom worked with Tom Branson. Michael Eastwood, Department of Pure Mathematics

Professor Michael Eastwood, University of Adelaide, South Australia  Wednesday, May 16th at 3:30 PM in Lecture Room VAN 301.

Title: Higher symmetries of the Laplacian. Abstract: Which linear differential operators preserve harmonic functions? Even on Euclidean space, this is a deceptively simple question. The answer may be expressed in terms of conformal geometry and the AdS/CFT correspondence. In particular, the structure of the algebra of such operators may be written as an explicit quotient of the universal enveloping algebra of the conformal algebra. The investigation is motivated by questions asked by Witten in relation to string theory. If time permits, I shall discuss higher symmetries of the Dirac operator and/or explain how twistor theory may be used as an approach in four dimensions. The article on which this talk is based can be found here (Annals of Mathematics 161 (2005) 1645-1665).