Advancing the Mathematical Field
American University's recent Characters, Lifting, and Types mathematics conference brought together 72 mathematicians, both leading scholars and junior researchers, from 18 states, four Canadian provinces, India, Israel, and the United Kingdom. The gathering was supported by the National Science Foundation.
Professor Jeffrey Adler, Mathematics and Statistics Department Chair, believes the conference directly contributed to the advancement of the mathematical field. “We wanted to bring together some of the top people in the field so that they can report on what they’ve been doing over the past few years,” said Adler. “But we also wanted to initiate junior researchers into the field.”
The conference comes as the culmination of a three year project conducted by Adler alongside AU mathematics professors Joshua Lansky and Jeffrey Hakim as a result of a Focused Research Group (FRG) grant the three received in 2009 from the NSF.
Conference mini-courses and speakers focused on a variety of mathematical concepts including: characters, types, symmetric spaces, and the Langlands correspondence. The study of these subjects and what connects them should ultimately help to unlock a variety of mathematical truths.
“Think of a situation where you have a bunch of miscellaneous facts,” said Adler, “and you believe that they are connected somehow, and that this connection will reveal an underlying truth. You don’t know what the connection is, so you don’t know the underlying truth. But you know something about the connection, thus some of the truth, and are trying to find out more.”
Lansky described the conference’s discussion of the concept of harmonic analysis. “Harmonic analysis is a facet of representation theory dealing with decomposing functions into superpositions of simper functions called characters,” said Lansky. “Some concrete examples include the decomposition of a sound wave into a superposition of pure tones, or the wave function of an electron into a superposition of basic quantum states. So the ideas from this area of math are all around us in the natural world.”
Adler believes the conference ultimately served an important purpose in further advancing the field by bringing together a variety of researchers. “No one has developed the Vulcan mind meld yet,” he said. “So although we can read each other’s papers and send each other e-mail, sometimes there’s no substitute for face-to-face discussion.”