• Speaker: Claude LeBrun
• Time: 9:00-10:00
• Abstract: Dimension four provides a surprisingly idiosyncratic setting for the interplay between scalar curvature and differential topology. This peculiarity becomes especially pronounced when discussing the Yamabe invariant or “sigma constant” of a smooth compact manifold; and Seiberg-Witten theory makes this especially apparent for those 4-manifolds that arise as compact complex surfaces. For compact complex surfaces of Kaehler type, I showed in the late 1990s that the sign of the Yamabe invariant is always determined by the Kodaira dimension, and calculated the Yamabe invariant exactly in all cases where it is non-positive. In this talk, I will describe recent joint work with Michael Albanese that generalizes these results to all complex surfaces of non-Kaehler type, except those of class VII. However, I will also explain why excluding this exceptional class is absolutely essential for these purposes.