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1. Wall-crossing for Calabi-Yau varieties


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      Problem 1.1.

      Exploit wall-crossing techniques to prove the DT/PT correspondence for Calabi-Yau 3-folds with tautological insertions.


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          Problem 1.2.

          Exploit wall-crossing to prove the rationality and symmetry of the PT invariants for Calabi-Yau 3-folds.


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              Problem 1.3.

              Let $X$ be a Fano 3-fold, and $K_X$ a local Calabi-Yau 4-fold, obtained as the canonical bundle of $X$. Prove DT/PT type correspondences on $X$ via wall-crossing for the Calabi-Yau 4-fold $K_X$.


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                  Problem 1.4.

                  Let $X$ be a Fano 3-fold, and $p:Y\to X$ an elliptically fibered Calabi-Yau 4-fold. Compute invariants, or prove correspondences on $X$ by performing wall-crossing on $Y$, with respect to classes on $Y$ pulled back from $p$.


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                      Problem 1.5.

                      Let $X$ be a Calabi-Yau 4-fold. Use wall-crossing to formulate new (conjectural) relations on DT and PT type invariants on $X$, extending the known (conjectural) DT/PT correspondences of Bae-Kool-Park.

                          Cite this as: AimPL: Wall-crossing: techniques and applications, available at http://aimpl.org/wallcrossing.