# Undergraduate Colloquium

**Fall 2014**

**Wednesdays 12:55 - 1:45**

**LCB 225**

Pizza and discussion after each talk

Receive credit for attending

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