Jim Bryan, University of British Columbia, The orbifold vertex: counting curves on orbifolds by counting piles of colored boxes

Abstract: Over the last few decades, sophisticated theories, often inspired by string theory, have been developed for counting curves on Calabi-Yau threefolds. For the particularly nice class of toric threefolds, these theories reduce to a beautiful combinatorial problem: how many different ways are there of piling n boxes in a corner? When the curve counting is considered for toric orbifolds, the combinatorial problem transforms into counting colored boxes. We will assume no knowledge of Calabi-Yau threefolds, toric geometry, orbifolds, or string theory. Experience stacking boxes in a moving van is helpful, but not necessary.