Calendar

I will define and review the basics of exponential networks associated to CY 3-folds described by conic bundles. I will focus mostly on the mathematical aspects and general ideas behind this construction as well as its conjectural connection with generalized Donaldson–Thomas invariants. This is based on joint work with S. Banerjee and P. Longhi.

In a series of papers, Aluffi and Faber computed the degree of the GL3 orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how these orbits degenerate, yielding a fairly complete picture in the case of plane quartics. As an enumerative consequence, we will see that a general genus 3 curve appears 510720 times as a 2-plane section of a general quartic threefold. We also hope to survey the relevant literature and will only assume the basics of intersection theory. This is joint work with M. Lee and A. Patel.

In this talk, we briefly review the distributional symmetries for *-random variables, which are defined by coactions of corepresentations of quantum groups. We classify all de Finetti type theorems for classical independence and free independence by studying vanishing conditions on the classical and free cumulants.  Examples for our de Finetti type theorems and approximation results in the spirit of Diaconis and Freedman are also provided.

In this talk, we will discuss the construction of Kahler Ricci flow on complete Kahler manifolds with unbounded curvature. As a corollary, we will discuss the application related to Yau’s
uniformization problem and the regularity of Gromov-Hausdorff’s limit. This is joint work with L.F. Tam.

— Organized by Professor Shing-Tung Yau