# 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 Ivan Sudakov
**Fractals in Nature**

*Abstract:*We discuss the mathematical concept of fractals and how fractals relate to issues within the Earthâ€™s climate system. A fractal is any equation or pattern, that when visualized, produces a similar image when viewed at any spatial scale. We describe how fractal-like patterns occur widely in nature and introduce the fractal dimension, a number which describes the fractal-like nature of an object. Specifically, we will highlight the ubiquitous nature of fractals within many facets of the climate system. We provide a real example of fractals in nature and involve our students to solving a few entertaining problems.- September 10 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 17 Kenneth Bromberg - Director of Graduate Studies
**Applying for and attending graduate school**

*Abstract:*This weeks Undergraduate Colloquium will be aimed at helping undergraduates answer the following questions:- Should I apply to graduate school?
- How do I apply to graduate school?
- What will it be like when I'm in graduate school?

- September 24 Peter Trapa

- October 1 Kelly MacArthur

- October 8 Aaron Bertram

- October 15 No Talk - Fall Break

- October 22 Vira Babenko

- October 29 Ben Trahan (NSA)
- Location Change to LCB 215 (this talk only!)

- November 5 Sean McAfee

- November 12 Peter Alfeld

- November 19 Stewart Ethier

- November 26 Shiang Tang

- December 3 Braxton Osting

- December 10 Anna Macquarie Romanova