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Canonical bases for cluster algebras

- M. Gross, P. Hacking, S. Keel, M. Kontsevich
- Mathematics
- 5 November 2014

In [GHK11], Conjecture 0.6, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical… Expand

Large Complex Structure Limits of K3 Surfaces

Motivated by the picture of mirror symmetry suggested by Strominger, Yau and Zaslow, we made a conjecture concerning the Gromov-Hausdorff limits of Calabi-Yau n-folds (with Ricci-flat K\"ahler… Expand

From real affine geometry to complex geometry

- M. Gross, Bernd S Siebert
- Mathematics
- 28 March 2007

We construct from a real ane manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking… Expand

The tropical vertex

- M. Gross, R. Pandharipande, Bernd S Siebert
- Mathematics
- 4 February 2009

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group are… Expand

Logarithmic Gromov-Witten invariants

- M. Gross, Bernd S Siebert
- Mathematics
- 21 February 2011

ing, now let π : Y → W be a proper morphism of schemes and let αi : Mi → OY , i = 1, 2, be two fine saturated log structures on Y . Consider the functor (2.1) LMorY/W (M1, M2) : (Sch/W ) −→ (Sets)… Expand

Topological mirror symmetry

- M. Gross
- Mathematics
- 2 September 1999

This paper focuses on a topological version on the Strominger-Yau-Zaslow mirror symmetry conjecture. Roughly put, the SYZ conjecture suggests that mirror pairs of Calabi-Yau manifolds are related by… Expand

Mirror symmetry for log Calabi-Yau surfaces I

- M. Gross, P. Hacking, S. Keel
- Mathematics
- 24 June 2011

We give a canonical synthetic construction of the mirror family to pairs (Y,D) where Y is a smooth projective surface and D is an anti-canonical cycle of rational curves. This mirror family is… Expand

Examples of Special Lagrangian Fibrations

- M. Gross
- Mathematics, Physics
- 1 December 2000

We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric… Expand

Mirror Symmetry via Logarithmic Degeneration Data I

- M. Gross, Bernd S Siebert
- Mathematics
- 4 September 2003

Introduction. 1 1. Derivations and differentials 6 2. Log Calabi-Yau spaces: local structure and deformation theory 16 2.1. Local structure 16 2.2. Deformation theory 25 3. Cohomology of log… Expand

Dirichlet Branes and Mirror Symmetry

- P. Aspinwall, T. Bridgeland, +7 authors P. Wilson
- Mathematics
- 4 November 2009

Research in string theory over the last several decades has yielded a rich interaction with algebraic geometry. In 1985, the introduction of Calabi-Yau manifolds into physics as a way to compactify… Expand

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