# Seminars & Events for Differential Geometry & Geometric Analysis Seminar

##### Limiting Properties of the Yang-Mills flow on Kahler Manifolds

In this talk, I will give a result about the limit of the Yang-Mills flow associated to a holomorphic vector bundle E over an arbitrary Kähler manifold (X;ω). In particular, this theorem says that the flow is determined at infi nity by the holomorphic structure of E. Namely, if we fix an integrable unitary reference connection A0 de fining the holomorphic structure, then the Yang-Mills flow with initial condition A0, converges (away from an appropriately defi ned singular set) in the sense of the Uhlenbeck compactness theorem to a holomorphic vector bundle E, which is isomorphic to the associated graded object of the Harder-Narasimhan-Seshadri ltration of (E;A0).

##### Isometries of Lie groups equipped with intrinsic distances

PLEASE CLICK ON SEMINAR TITLE FOR COMPLETE ABSTRACT. We consider Lie groups equipped with distances for which every pair of points can be join with an arc with length equal to the distance of the two points. These distances are generalizations of Riemannian distances.

##### Singular special Lagrangian n-folds

Special Lagrangian n-folds are high-dimensional volume minimizing submanifolds discovered around 1982 by Harvey and Lawson in their pioneering work on calibrations. More recently special Lagrangians n-

folds have played an important role in developments at the interface of geometry and string theory related to Mirror Symmetry. Singular special Lagrangian n-folds play a key role in these development but

are still relatively poorly understood. This talk will give an introduction to special Lagrangian geometry and singular special Lagrangian n-folds and will then focus on joint work with Nicos Kapouleas that uses geometric PDE gluing methods to construct a plethora of new singular special Lagrangians (cones) in dimensions 3 and higher.