Ionut Ciocan-Fontanine

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We construct new “virtually smooth” modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental’s compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by(More)
Following the work of Okounkov-Pandharipande [OP1, OP2], Diaconescu [D], and the recent work [CDKM] studying the equivariant quantum cohomology QH∗ (C∗)2(Hilbn) of the Hilbert scheme and the relative Donaldson-Thomas theory of P ×C, we establish a connection between the J-function of the Hilbert scheme and a certain combinatorial identity in two variables.(More)
Abstract. Based on the ideas in [CKP], we introduce the weighted analogue of the branching rule for the classical hook length formula, and give two proofs of this result. The first proof is completely bijective, and in a special case gives a new short combinatorial proof of the hook length formula. Our second proof is probabilistic, generalizing the (usual)(More)
The famous hook-length formula is a simple consequence of the branching rule for the hook lengths. While the Greene-Nijenhuis-Wilf probabilistic proof is the most famous proof of the rule, it is not completely combinatorial, and a simple bijection was an open problem for a long time. In this extended abstract, we show an elegant bijective argument that(More)
We provide a short introduction to the theory of ε-stable quasimaps and its applications via wall-crossing to Gromov-Witten theory of GIT targets. Mathematics Subject Classification (2010). Primary 14D20, 14D23, 14N35.