Surf's Up

If you could not even conceive of a way to answer the question “Is every finite group realizable as a Galois group over the rational numbers?”—if you don’t even know what it means—then you might find the odds of someone winning a speaking competition on that topic pretty slim. Yet, at the 2006 Doris Perpall Summer Undergraduate Research Fellowship (SURF) Speaking Competition, sophomore Po-Ling Loh, a math major from Madison, Wisconsin, bagged her second first prize in a row for a math talk. It was a banner year for the subject, in fact: one of the two third-prize winners also talked about math, and this is only the second year since the competition began in 1993 that mathematics speakers have won prizes.

The details of Loh’s project, in an obscure but important field of math called Galois theory, seemed to sail above the heads of the audience members. But Loh kept them enchanted with stories, such as how legendary mathematician Evariste Galois died in 1832 at age 20 in a duel with an artillery officer over a woman—but not before recording his ideas the night before. Loh’s public-speaking skills are so strong that she needs no show-and-tell props to win over her audience, but she brought some anyway, demonstrating how origami folding can successfully trisect an angle where a simple compass and straightedge fail at the task. (See E&S, 2004, No. 1, p. 10 for how to do this at home.)

Mercilessly titled Q-Admissibility of PSL(2,q), the algebraic abstraction that was Loh’s project required constructing a polynomial equation with many variables in just such a way that they would factor in a specified pattern. The pattern forms the so-called “Galois group” of the polynomial, and it’s part of a fundamental problem that has perplexed mathematicians since long before Galois murkily drafted his thoughts on the matter. Bandying about terms like “Sylow p-subgroup” and “maximal subfield of a Q-division algebra,” it was hard to believe Loh’s claim that a lack of higher math skills prevented her from solving the challenge. But she will keep plugging away, taking more math classes and attacking another SURF challenge, on a related math topic, this summer. “For now, I’m just focusing on the theory of my research, rather than its applications,” she says.

The second prize went to Alex Huth, a senior in computation and neural systems who hopes to pursue further studies in Sweden. His research, which used functional Magnetic Resonance Imaging (fMRI) to mark contrasts in the responses of the visual cortex in the brains of blind and sighted people, was easier to grasp. One subject, a blind man who employs bat-style echolocation to ride a bicycle, also had quite a sense of humor, Huth recalls. “We asked how the train ride to Pasadena had been, to which he replied, ‘The view was horrible.’”

Huth’s seven sighted subjects responded as one might expect—their visual cortexes lit up when they looked at moving objects. Surprisingly, though, the visual cortexes of the five blind subjects lit up in response to moving sounds, suggesting that this area of the brain keeps working even though its manner of use changes. Huth was lucky enough to work with an additional two subjects who were blind most of their lives but gained vision in their fifties. These fMRI scans seem to have captured brain reorganization in progress—their subjects’ visual cortexes responded to both visual and auditory signals. Huth will continue to work on the subject with mentors Melissa Saenz (BS ’98), a postdoc in biology, and Christof Koch, the Troendle Professor of Cognitive and Behavioral Biology and professor of computation and neural systems. “In the coming era of sensory rehabilitation—retinal implants for the blind are gaining some traction, and cochlear implants for the deaf are already very advanced—it’s becoming increasingly important to study how the brain adapts to such major changes,” Huth says.

Tied for third place were freshman Evan Gawlik and senior Arturo Pizano. Gawlik tackled the three-body problem—an infamous conundrum dealing with the motions of three masses in space subject to mutual gravitational attraction—by comparing the accuracy of different numerical methods that try to predict them. In a configuration in which one mass dominates, like the sun in the sun–Earth–moon system, it’s relatively straightforward to predict orbits. But when the three masses closely match, their movements are somewhat chaotic and much harder to predict—even when the problem is simplified by considering one mass to be negligible, as Gawlik did.

Pizano studied folding in cytochromes, which are a large family of proteins that, even though their amino acid sequences are similar, all fold their own way. This is a great mystery, as it is the attractions between the amino acids that make proteins fold, so proteins with similar sequences should fold into similar shapes. Within this greater problem lies the subplot of Cytochrome c–b₅₆₂, the particular class that Pizano studied. While these proteins do have similar folded structures, each accomplishes the task in a different manner. Pizano will continue to pursue the dilemma until he graduates this June.

The runners-up were Matthew Lew, who devised a device for the study of optics, Diana Lin, who tested a model of a signaling pathway in cells, and Andrew Kositsky, who mathematically reconstructed the 20th-century record of slip distribution along the Sumatra fault. —EN