Mathematics major Joel Specter ’11 is ahead of the program. Despite only finishing his junior year at Wesleyan, he’s already completed all first-year graduate courses for the department’s Ph.D. program.
“When discussing mathematics with him it becomes clear that he is already thinking like a mathematician in a very serious way that one rarely sees in students until well into their graduate careers,” says Specter’s advisor David Pollack, associate professor of mathematics.
For Specter’s achievements in mathematics, he was awarded with a Barry M. Goldwater Scholarship for the 2010-11 year.
Congress established the Goldwater Scholarship and Excellence in Education Program in 1986 to honor Senator Barry M. Goldwater. The program provides a continuing source of highly qualified scientists, mathematicians, and engineers by awarding scholarships to college students who intend to pursue careers in these fields.
Specter studies a mathematical structure called a “Lubin-Tate formal group,” named after Jonathan Lubin, professor of mathematics at Brown University and John Tate, who won the 2010 Abel prize for lifetime achievement in mathematics. A formal group is a two variable power series (infinite degree polynomial) which describes an “alternate” addition rule one can impose in certain settings.
A Lubin-Tate formal group allows researchers to build auxiliary data which describes symmetries in certain objects. Specter wants to prove that a formal group exists in the background whenever one is given data that seems to be describing such symmetries.
Specter says his research is motivated by conceiving clever ideas rather than generalizing the behavior of examples.
“This has caused me to grow tremendously as a mathematician,” Specter says. “However, the most important reason for this research, something that can be said about all investigations into the unknown in mathematics, is that it is not known why it is important. I don’t know what results the techniques I hope to discover will be used to do … Research is little about a search for proof, but very much about those ideas which arise in the search.”
Specter’s investigation is a continuation of research done at the National Science Foundation-funded Claremont Colleges Mathematics Research Experiences for Undergraduates June 8 through July 31, 2009. There, Specter worked under Professor Ghassan Sarkis of Pomona with students Minsoo Kim of Pomona, Emily Ognacevic of the University of St. Louis, Jessica Olsen of the University of Puget Sound and Sam Schiavone of Amherst College.
He and Professor Sarkis are collaborating on a paper, and they will be meeting this summer to discuss further directions for their work.
“I am deeply indebted to each of these people as well as my time spent at the Claremont Colleges,” Specter says.
During the 2009-10 academic year, Specter worked on the project primarily on his own while consulting the Math Department’s faculty.
“Joel really is an extraordinary student,” Pollack says. “He has a great talent for mathematics, and is constantly working to learn more and deepen his understanding. Joel has managed to prove the result he’s aiming towards in some special cases. It’s a very nice piece of work, and will surely wind up getting published.”
Next fall, Specter will participate in the Visiting Undergraduate Student Program at Harvard University, where he will be taking more graduate level mathematics courses. Specter’s career goal is to have a Ph.D in mathematics and conduct research in pure mathematics and teach at the university level.