Geometric Analysis and Topology Seminar

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Calibrations and Blow Up Analysis

Speaker: Costante Bellettini, Princeton

Location: Warren Weaver Hall 202

Date: Tuesday, November 26, 2013, 2 p.m.

Synopsis:

Calibrated currents naturally appear when dealing with several geometric questions: Plateau's problem was probably the first connection, but recent years have witnessed the birth of new sources of interest, for example Taubes's work on Seiberg-Witten and Gromov invariants or some special setting for high dimensional gauge theory (such as anti self-dual instantons). Some aspects of these geometric problems require a deep understanding of regularity properties of calibrated currents. The issues are generally very hard. We will focus on some particular cases, where we will show a surprising connection with pseudo-holomorphic currents and perform a blow up analysis, leading to the uniqueness of tangent cones and an explicit rate of decay for the mass ratio.