Thursday, May 7th, 2015
03:00pm - 4:00pm, in McCormack 02-420

Eric Grinberg

UMass Boston

Integral Geometry in Outer Space

Abstract: ntegral Geometry goes back to the Buffon Needle Problem (circa. 1776). It has two main branches, which are related. One focuses on geometric objects such as curves, surfaces, etc., and their measures (length, areas, etc.). The other deals with functions and properties reflected in their integrals. The basic mathematical principles that power imaging devices such as CAT (Computer Aided Tomography) scanners and MRI (Magnetic Resonance Imaging) scanners are built on integral geometry of the second kind. This subject overlaps a number of mathematics fields, both pure and applied. In this presentation we will focus on one fairly concrete instance of integral geometry, replacing three dimensional space with a manifold called Complex Projective Space (CP^n), and exploring the analog of CAT scanners in it. In part, this will be an opportunity to `get to know a manifold'--how do we do calculus in it? Can we compute enough to obtain an analog of a CAT scanner reconstruction? Come and See.