64th Annual STS (2004-2005)
Finalists
Abhi Gulati

ILLINOIS
Abhi Gulati, 18, of Bloomington submitted a mathematics project in the Intel Science Talent Search that involves algebra and combinatorics, and extends his earlier work on the SET card game. In SET, three cards are a set if they are all the same, or all different, with regard to certain attributes. This translates in the setting of groups to a condition of the form x1 + x2 + x3 = 0 where the x's come from copies of the cyclic group of order 3. Abhi develops a general version of this condition in the language of groups and hypergraphs. A hypergraph is like a graph, but the sets of vertices with a common edge are replaced by k-element sets of vertices for some fixed k >= 2. Abhi applies combinatorial results to prove that certain colorings of a hypergraph on a finite abelian group can have no monochromatic edges. Abhi is a violinist and student council member at the Illinois Mathematics and Science Academy in Aurora and has perfect SAT scores. Born in India, he is the son of Rakesh and Radha Gulati. He hopes to attend Harvard and go on to receive his graduate degree in mathematics. Abhi plans to become a professor, so that he can continue his research while teaching.