I will recall the definition of cluster algebra, and then reformulate the theory in terms of birational geometry of affine CY manifolds. Then I'll explain how the Fock-Goncharov conjectures on canonical dual bases are a special case of the general mirror conjecture from my GADGET talk, and deduce from our theorem the rank 2 case of their conjecture.

The 2-periodic dg-category MF of matrix factorizations is a categorical singularity invariant, appearing on the algebro-geometric side of mirror symmetry. After recalling some categorical background, we'll explain the results in the title and how they're useful for establishing basic properties of MF and for relating its Hochschild invariants to classical linear-algebraic invariants of singularities. Finally, we'll give a description of MF in terms of "derived algebraic geometry," and see how this allows one to give conceptual proofs of the results in the title.

We will discuss the special role played by Ricci curvature in complex geometry, especially in relation to Calabi-Yau manifolds, and discuss several problems that arise naturally in this area. (The speaker is an Assistant Professor candidate).

If we have a smooth compact manifold, then its cotangent bundle has a natural symplectic form. A smooth affine variety also has a natural symplectic form. We construct many cotangent bundles that are not symplectomorphic to smooth affine varieties. Examples include cotangent bundles of simply connected n-manifolds with at least one Betti number greater than that of the n-torus. The main tool used to distinguish these objects is called wrapped Floer cohomology.