Abstracts

Ray optics, geodesics, and curved space

Steve Trettel (Stanford University)

Friday, February 26, 7:30pm PST

To a first approximation, the behavior of light appears quite simple: it always travels in a straight line from the source to the viewer. But upon deeper inspection - various surprising effects - from mirrors to mirages, show the need for a more sophisticated theory. These seemingly disparate phenomena are consequences of a single underlying principle: in every circumstance light endeavors to take the most efficient path between two points, or the path of least flight time.

From this observation springs forth a deep connection of the theory of ray optics to differential geometry, modeling the trajectory of light in a varying medium as the shortest path - or geodesic- in an abstract curved space.

In this talk we will demonstrate the power of this viewpoint, producing computer simulations of lenses and mirages by solving for geodesics in the appropriate metric. Finally, we investigate telltale signs of curvature in the real world — including ring-like mirages appearing in images from the Hubble space telescope, and consider Einstein's great insight: that gravity is not a force, but just a consequence of living in a curved world.

Intentionally bringing diversity awareness into the classroom

Hortensia Soto (Colorado State University)

Saturday, February 27, 2:00pm PST

We are in an era where we are intentionally trying to address the need to embrace diversity, especially in the STEM disciplines. Initiatives to address this need include hiring faculty of color, inviting speakers of color to national meetings, having mission statements that address diversity, etc. These are all wonderful efforts that support diversity. In my presentation, I discuss the value of identifying with others, looking inward, and reflecting on how our own experiences can be used to support diversity in STEM disciplines. Specifically, I will share my efforts to do this with my history of mathematics students, who are prospective secondary teachers and have an opportunity to influence generations to come.