More than 60 mathematicians and mathematics graduate students are expected to arrive at the Homewood campus today for a five-day conference on Stark's conjectures, a series of bridges between two areas of mathematical theory first developed by Harold Stark, one of the conference's main speakers.
Stark began to develop the conjectures in the 1970s while at MIT. They involve constructing links between two apparently unrelated aspects of number theory: analytic number theory, which centers on the study of continuous functions called L-functions that move from value to value without missing any of the intermediate values; and algebraic number theory, which focuses on functions that move from one discrete value to another without landing on any of the values in between.
The conjectures have a number of applications in cryptography and coding theory, according to Cristian Popescu, assistant professor of mathematics in the Krieger School of Arts and Sciences.
"Every crypto-system out there is based on a certain number theoretic algorithm, so there are plenty of practical applications to all this," said Popescu, who chaired the conference organizing committee and will be one of the main speakers. "In fact, number theory is one of the few branches of pure mathematics where research is supported by the National Security Agency."
Popescu said progress since the 1970s in developing Stark's conjectures, now viewed as one of the most central unresolved questions in number theory, has been uneven, with surges of activity followed by periods of inactivity.
"We happen to be in the middle of a period of intense activity, and this is why my co-organizers and I found this to be the right time for organizing a conference," he said.
Popescu said the committee wanted to have the conference at Hopkins to increase the number of graduate students who could attend.
"We hope that some of these graduate students will become interested in this technique and come up with new ideas," he explained.
In addition to Stark, now at the University of California-San Diego, other eminent speakers for the conference will include John Tate of the University of Texas at Austin, Karl Rubin of Stanford and Benedict Gross of Harvard. Tate and Stark are members of the National Academy of Science, and Rubin, Tate and Gross are winners of the prestigious Cole Prize in Number Theory.
The conference is supported by grants from the National Science Foundation, the Number Theory Foundation and Johns Hopkins.