Logarithmic Transformations and Vector Bundles on Elliptic Surfaces via O-Minimal Geometry II

Explore the intricate relationship between logarithmic transformations and vector bundles on elliptic surfaces through the lens of o-minimal geometry in this one-hour lecture. Delve into Kodaira's groundbreaking operation from the 1960s, which allows for the creation of elliptic surfaces with multiple fibers. Examine the significance of vector bundles on elliptic surfaces across various mathematical disciplines, including algebraic geometry, gauge theory, and mathematical physics. Gain insights into ongoing research, including joint works with L. Katzarkov and E. Lupercio, that investigates how specific vector bundles on elliptic surfaces transform under logarithmic transformations, utilizing the framework of o-minimal geometry.