The crepant transformation conjecture implies the monodromy conjecture

The Crepant Resolution Conjecture

For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the GromovWitten theories of the orbifold and the resolution. We prove the conjecture for the equivariant Gromov-Witten theories of Sym n C2 and Hilbn C2 .

The Füredi–Hajnal Conjecture Implies the Stanley–Wilf Conjecture

We show that the Stanley–Wilf enumerative conjecture on permutations follows easily from the Füredi–Hajnal extremal conjecture on 0-1 matrices. We apply the method, discovered by Alon and Friedgut, that derives an (almost) exponential bound on the number of some objects from a (almost) linear bound on their sizes. They proved by it a weaker form of the Stanley–Wilf conjecture. Using bipartite g...

The Graham Conjecture Implies the Erdös-turán Conjecture

Erdös and Turán once conjectured that any set A ⊂ N with

The Bochner-riesz Conjecture Implies the Restriction Conjecture

Lectures on Gromov-witten Theory and Crepant Transformation Conjecture

These are the pre-notes for the Grenoble Summer School lectures June-July 2011. They aim to provide the students some background in preparation for the conference. Nominally, only the basic knowledge on moduli of curves covered in the first week is assumed, although I tacitly assume the students either have heard one thing or two about the subjects, or are formidable learners. It is well-nigh i...