- The following speakers are confirmed:
- Tristan Collins (MIT)
- Title: Results in Strominger-Yau-Zaslow Mirror Symmetry
Mirror symmetry originally arose as a mysterious duality between Calabi-Yau threefolds, interchanging complex and symplectic structures. This duality has since expanded to include a much broader collection of objects, including Fano manifolds, and Landau-Ginzburg models. Two fundamental themes in mirror symmetry are (1) the existence of special Lagrangian fibrations, as conjectured by Strominger-Yau-Zaslow and (2) the correspondence between “stable” objects as predicted in work of Thomas-Yau, and Douglas. Here, stable objects are meant to be special Lagrangian manifolds on the symplectic side, and holomorphic bundles with canonical metrics, on the complex side. I will report on recent results in both of these directions. This talk with discuss joint works with A. Jacob, Y.-S. Lin, and S.-T. Yau.
- Blaine Lawson (Stony Brook)
- Title: The Special Lagrangian Potential Equation
- Peter Petersen (UCLA)
- Title: Alexandrov Spaces with Maximal Boundary
The talk will cover recent work with Karsten Grove about Alexandrov spaces with boundary. The questions are related to geometric versions of the “Positive Mass Conjecture”. There are two interesting problems that we’ll discuss:
How does one bound the area of the boundary or the size of an Alexandrov space with boundary with only local conditions.
What happens when the boundary has maximal area or the space has maximal size?
- Colleen Robles (Duke)
- Title: What representation theory can tell us about the cohomology of a hyperkahler manifold
The cohomology (with complex coefficients) of a compact kahler manifold M admits an action of the algebra sl(2,C), and this action plays an essential role in the analysis of the cohomology. In the case that M is a hyperkahler manifold Verbitsky and Looijenga—Lunts showed there is a family of such sl(2,C)’s generating an algebra isomorphic to so(4,b_2-2), and this algebra similarly can tell us quite a bit about the cohomology of the hyperkahler. I will describe some results of this nature for both the cohomology of O’Grady’s 10-dimensional hyperkahler and Nagai’s conjecture on the nilpotent logarithm of monodromy arising from a degeneration. This is joint work with Mark Green, Radu Laza and Yoonjoo Kim.