# Mathematical Sciences Research Institute

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# Seminar

Combinatorics of Donaldson–Thomas and Pandharipande–Thomas invariants January 23, 2012 (04:10 PM PST - 05:00 PM PST)
Parent Program: -- UC Berkeley, 60 Evans Hall
Speaker(s) Benjamin Young (University of Oregon)
Description No Description
Video
I will discuss a combinatorial problem which comes from algebraic geometry. The problem, in general, is to show that two theories for "counting" curves in a complex three-dimensional space X (Pandharipande–Thomas theory and reduced Donaldson–Thomas theory) give the same answer. I will prove a combinatorial version of this correspondence in a special case (X is toric Calabi–Yau), where the difficult geometry reduces to a study of the topological vertex\'\' (a certain generating function) in these two theories. The combinatorial objects in question are plane partitions, perfect matchings on the honeycomb lattice and related structures.