## Newsroom

## Five Students Give Talks at MAA MathFest

Students give talks at the national Mathematical Association of America MathFest meeting in Portland, OR.

Five Southwestern students, Darren Allen (Junior, Comp. Math. Major), Stephen Foster (recent graduate, CS major), Tommy Rogers (Senior, CS+Math double major), Sarah Stern (Senior, Math Major) and Sean Watson (Senior, Math Major) gave research presentations and expository talks at the annual national Mathematical Association of America (MAA) MathFest meeting in Portland, OR, August 5-8. They were funded by Pi Mu Epsilon National Honors Society, MAA, and Southwestern. In addition to giving talks, they attended a number of interesting talks by other students from around the country and presentations by renowned mathematicians. They also tasted a number of interesting doughnuts at Voodoo Doughnuts.

Sean Watson received a Pi Mu Epsilon Excellent Speaker Award for his presentation on research that he did for 8 weeks over the summer with Dr. Fumiko Futamura. He was awarded $150 and a hearty handshake from the President of Pi Mu Epsilon.

The titles and summaries of the student talks are listed below.

Darren Allen: “Finite Frame Cryptography”

Frame theory is used in many signal processing applications including image compression, reduc-

ing unwanted noise, and sending data over the Internet. Very recently, attempts have been made to

utilize frames as a piece of cryptographic machinery. We present a brief overview of finite frames

and some experimental cryptographic systems involving finite frame theory with an explanation of

why these are not particularly effective.

Stephen Foster: “America’s New Calling: Modeling the Energy Impact of the Cell Phone Revolution”

The ongoing cell phone revolution warrants an examination of its energy impacts past, present,

and future. Thus, we have developed a model which adheres to two requirements: it can evaluate

energy use since 1990; and it is flexible enough to predict future energy needs. Mathematically

speaking, our model treats households as state machines and uses actual demographic data to guide

state transitions. We produce national projections by simulating multiple households. Our bottom-

up approach remains flexible, allowing us to: 1) model energy consumption for the current United

States, 2) determine efficient phone adoption schemes in emerging nations, 3) assess the impact of

wasteful practices, and 4) predict future energy needs.

Tommy Rogers: “Reconstructing Sparse Signals from Random and Incomplete Frequency Samples”

Compressive sensing advances a method for simultaneous signal acquisition and compression by

exploiting the sparsity of natural signals. A random frequency sample obtained using the Bernoulli

model can be used to reconstruct a much larger signal with a very high probability by solving a

convex optimization problem.

Sarah Stern: “Labelings of Directed Graphs”

Graph labeling has been widely researched over the last 50 years. Recently graceful and magic

labelings for directed graphs have been defined and studied. This talk will focus on some new

labelings of directed graphs. Definitions and examples will be given.

Sean Watson: “The Structures of Series and Sum Ranges in Banach Spaces”

The famous Riemann theorem states that a conditionally convergent series in R can be rearranged

to converge to any real number. In a finite dimensional Banach space (a space complete with

respect to its norm), an analogue of the Riemann theorem, the Levy-Steinitz theorem, will be pre-

sented. An introduction to the infinite-dimensional case, examples of when the analogy breaks

down, and ongoing research into understanding when the Levy-Steinitz theorem holds will also be

discussed.