Facebook has over 700 million users with almost 70 billion connections. The hard part isn.t people making friends; rather it.s Facebook.s computers storing and accessing relevant data, including information about friends of friends. The latter is important for recommendations to users (People You May Know). Much of this work involves computer science, but mathematics also plays a significant role. Subjects such as linear programming and graph theory help cut in half the time needed to determine a person.s friends of friends and reduce network traffic on Facebook.s machines by about two-thirds. What.s not to like? The probability of people being friends tends to decrease as the distance between them increases. This makes sense in the physical world, but it.s true in the digital world as well. Yet, despite this, the enormous network of Facebook users is an example of a small-world network. The average distance between Facebook users the number of friend-links to connect people is less than five. And even though the collection of users and their connections may look chaotic, the network actually has a good deal of structure. For example, it.s searchable. That is, two people who are, say, five friend-links away, could likely navigate from one person to the other by knowing only the friends at each point (but not knowing anyone.s friends of friends). For More Information: Networks, Crowds, and Markets: Reasoning about a Highly Connected World, David Easley and Jon Kleinberg, 2010.

Many of today.s most striking buildings are nontraditional freeform shapes. A new field of mathematics, discrete differential geometry, makes it possible to construct these complex shapes that begin as designers. digital creations. Since it.s impossible to fashion a large structure out of a single piece of glass or metal, the design is realized using smaller pieces that best fit the original smooth surface. Triangles would appear to be a natural choice to represent a shape, but it turns out that using quadrilaterals.which would seem to be more difficult.saves material and money and makes the structure easier to build. One of the primary goals of researchers is to create an efficient, streamlined process that integrates design and construction parameters so that early on architects can assess the feasibility of a given idea. Currently, implementing a plan involves extensive (and often expensive) interplay on computers between subdivision.breaking up the entire structure into manageable manufacturable pieces.and optimization.solving nonlinear equations in high-dimensional spaces to get as close as possible to the desired shape. Designers and engineers are seeking new mathematics to improve that process. Thus, in what might be characterized as a spiral with each field enriching the other, their needs will lead to new mathematics, which makes the shapes possible in the first place. For More Information: .Geometric computing for freeform architecture,. J. Wallner and H. Pottmann. Journal of Mathematics in Industry, Vol. 1, No. 4, 2011.

James Sethian and Frank Morgan talk about their research investigating bubbles.

Muthu Alagappan explains how topology and analytics are bringing a new look to basketball.

Van Wedeen talks about the geometry of the brain's communication pathways.

Nazareth Bedrossian talks about using math to reposition the International Space Station.

Despite the considerable variety among cities, researchers have identified common mathematical properties that hold around the world, regardless of a city.s population, location or even time.

Colin Adams talks about knot theory

Lydia Bourouiba talks about surface tension and the transmission of disease

Researcher: Christopher Butson, Scientific Computing and Imaging Institute, University of Utah. Christopher Butson talks about work he's done to help treat Parkinson's disease.

Researcher: Cristina Stoica, Wilfrid Laurier University
Description: Cristina Stoica talks about celestial mechanics.

Researcher: Thomas Snitch, University of Maryland
Description: Thomas Snitch talks about nabbing poachers with math.
Audio files: podcast-mom-poaching-1.mp3 and podcast-mom-poaching-2.mp3

Researcher: Andrew Beveridge, Macalester College
Moment Title: Dis-playing the Game of Thrones
Description: Andrew Beveridge uses math to analyze Game of Thrones.

Researcher: Daniel Rothman, MIT. Dan Rothman talks about how math helped understand a mass extinction.

Researcher: Michel C. Molinkovitch, University of Geneva Description: Michel C. Milinkovitch used math, physics, and biology for an amazing discovery about the patterns on a lizard's skin.

Steven Strogatz and Mary Bushman talk about math's role in controlling HIV and understanding malaria, respectively. Mary Bushman says, "It's really cool to try and use math to nail down some questions that have gone unanswered for a really long time."

Report of the Fourth Meeting of the Conference of the Parties to the Convention on Biological Diversity Serving as the Meeting of the Parties to the Cartagena Protocol on Biosafety (Advance text)