December 12, 2008
Mathematics-based research projects, either individual or tandem, comprised one quarter of this year's dozen Siemens Competition finalists.
Senior Eric K. Larson of South Eugene High School garnered the highest spot for a mathematics project. He took second place—a silver medal and $50,000—for his individual research project, "The Classification of Certain Fusion Categories."
Fusion categories are a newer type of complex algebraic structure, which have applications in theoretical physics, computer science, and mathematics, notably in string theory, quantum computation, and knot theory. They represent a far-reaching generalization of groups, which are the algebraic structures often used to model symmetries. Larson identified a class of fusion categories containing non group-theoretic examples.
Larson credited Arkady Vaintrob of the University of Oregon with spurring his interest in algebra. He had won a silver medal at the 48th International Mathematical Olympiad and had attended the Math Olympiad Summer Program since the eighth grade.
Senior Ashok Cutkosky of David Henry Hickman High School, in Columbia, Mo., took fifth place and $20,000 for his project "Associated Primes of the Alexander Dual of Hypergraphs." In order to reveal the the intrinsic structure of hypergraphs, Cutkosky took an algebraic approach and worked to restate geometric properties of multivariable polynomials. His results have potential applications in issues such as the sharing of limited resources.
Cutkosky, whose parents are mathematicians, had taken first and second at the Great Plains Math League State Competition and received a silver medal in 2007 at the USA Mathematical Talent Search.
Raphael-Joel Lim (Indiana Academy for Science, Math, and Humanities, Muncie) and Mark Zhang (William P. Clements High School, in Sugar Land, Texas) took 5th place and $20,000 for their team project titled "Previously Unknown Parts of the Greene-Kleitman Partition for the Tamari Lattice." Their research answered a five-year-old mystery about the thickness of a fundamental mathematical structure called the Tamari lattice.
The two young mathematicians had met at the Texas Mathworks Honors Summer Math Camp, which emphasizes mathematical research. At the camp they worked with Director Max Warshauer.
Nearly 1900 students had registered to enter the 2008 Siemens Competition in mathematics and science, and 1200 research projects had been submitted for consideration. One hundred of the country's brightest high school students were eventually selected for the last round of competition. The National Finalist Award Presentation took place at New York University on Dec. 8, 2008.
Source: Siemens Foundation, Dec. 8, 2009.