THE UNIVERSITIES OF SYDNEY AND NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS ___________________JOINT COLLOQUIUM______________________ Speaker: Prof. Marius Mitrea (University of Missouri, USA) Title: Singular Integral Operators and Boundary Value Problems: Recent Progress Date: Monday, 27 JULY 200 Time: 1:00 pm Venue: Room 275 Carslaw Building, University of Sydney The talk will be preceded by lunch with the speaker. We will meet at 11:40 on the outdoor Plaza on the 2nd floor of Carslaw for lunch beforehand at the restaurant Thai@home on Glebe point Road. Abstract: I will review some of the historical developments in the area at the interface between Partial Differential Equations and Harmonic Analysis, with emphasis on the role played by boundary integral methods in the treatment of elliptic problems. The goal is to highlight the significance of tools from Harmonic Analysis which have played a fundamental role in establishing progressively sharper results in this field. The lecture is largely self-contained and accessible to nonspecialists.