Math Major Zeroes in on Class of ’21 Award

By Chris Lydgate '90 | September 1, 2015

Mathematics major Maddie Brandt ’15 won the Class of ’21 Award for her thesis on the Erdős-Ko-Rado theorem. The award recognizes “work of notable character, involving an unusual degree of initiative and spontaneity.”

Maddie’s thesis carries the rather imposing title “Intersecting Hypergraphs and Decompositions of Complete Uniform Hypergraphs.” As Prof. David Perkinson [1990–] explains:

Maddie’s thesis topic is extremal combinatorics, an area of mathematics with connections to information/computer science, biology, and statistics . . . It had been suggested to her that a certain result known as the Baranyai theorem might somehow be used to prove the Erdős-Ko-Rado theorem, and Maddie set out to see if that was true.

Her systematic attack on the problem is impressive. She collected and explained seven different known proofs of the Erdős-Ko-Rado theorem in order to understand the range of relevant ideas.  She goes on to present why one might hope that the Baranyai theorem might imply Erdős-Ko-Rado, then figures out a way to do a (nontrivial) computer search to find examples that show there is no way this hope can be realized. So at this point, she has solved the problem that had been posed to her, unfortunately, in the negative. I would like to emphasize that this resolution to the problem is almost certainly more difficult than if the result had been positive. Nonetheless, not content with that resolution, she considered what minimal generalization of the Baranyai theorem would be needed to actually prove Erdős-Ko-Rado. In this way, she independently discovered what turns out to be known in the literature as the wreath conjecture. An original result of her thesis is to show that the wreath conjecture is sufficient to prove Erdős-Ko-Rado.

Maddie wrote her thesis with Prof. Angélica Osorno [2013–].

Literature-theatre major Leah Artenian ’15 also won the Class of ’21 Award this year.

Tags: Students, Academics, Awards & Achievements, Thesis