The 2019 Robbins Prize of the American Mathematical Society will be awarded to Roger Behrend and collaborators Ilse Fischer and Matjaļ Konvalinka.
The prize, that is awarded every three years, will be given for their paper “Diagonally and antidiagonally symmetric alternating sign matrices of odd order,” published in 2017 in Advances in Mathematics (Vol. 315, pp. 324-365). In this work, Behrend, Fischer and Konvalinka prove, after more than 30 years, the conjectured formula for the number of odd-order diagonally and antidiagonally symmetric alternating sign matrices (ASMs), the last remaining of David Robbins’ conjectures on alternating sign matrices.
The Robbins conjectures have led to the development of new methods of enumeration, as well as to the discovery of deep connections to statistical physics. All of the conjectures had been proven by 2006, with the exception of the conjecture for diagonally and antidiagonally symmetric ASMs, which had resisted proof until the present paper. Not only is the paper a crowning achievement that makes use of deep methods developed by a community of researchers over more than 25 years, it is also a paper that makes new problems accessible.