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Our Brilliant Students

Math Major Zeroes in on Class of 鈥�21 Award

By Chris Lydgate '90
Brandt

Mathematics major   won the illustrious Class of ’21 Award for her senior thesis on the Erdös-Ko-Rado theorem.

The award recognizes “creative 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.” Scratching our heads, we turned to Prof. David Perkinson[mathematics 1990–] for an explanation. He wrote:

Maddie’s thesis topic is extremal combinatorics, an area of mathematics with connections to information/computer science, biology, and statistics. It has a long history in the Hungarian school of mathematics, and Maddie’s interest clearly grew out of her experience during a Budapest Semester in Mathematics. Unfortunately, none of us in the mathematics department has expertise in this area—so Maddie was essentially on her own . . . It had been suggested to her that as 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 to 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 (non-trivial) computer search to find examples that show there 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. Angelica Osorno [mathematics 2013–].

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