Undergraduate Colloquium

Fall 2014
Wednesdays 12:55 - 1:45
LCB 225

Pizza and discussion after each talk
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Past Colloquia

August 27    No Talk

September 3     Andrejs Treibergs
Mapping the Earth
Abstract: Can regions on the surface of the earth be mapped to the plane in such a way as to preserve areas, angles and lengths, i.e., by local isometries? We develop notions from the differential geometry of the sphere such as curvilinear coordinates, metric and length. We show that local isometries from the sphere to the Euclidean plane are impossible because if they existed, a natural compatibility condition on the metric would have to be satisfied: the curvature would have to vanish. We give examples of maps that preserve areas but not angles such as the one discovered by Lambert, and examples of maps that preserve angles but not areas such as the one first drawn by Mercator. We consider a notion of map distortion and discuss the theorem of Milnor, that for maps of spherical caps, the least distortion occurs for the azimuthal equidistant projection.

Lecture slides are available: http://www.math.utah.edu/~treiberg/MappingtheEarthSlides.pdf

September 10    

September 17    

September 24    

October 1    

October 8    

October 15     No Talk - Fall Break

October 22    

October 29    

November 5    

November 12    

November 19    

November 26    

December 3    

December 10