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

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 the significance of logarithmic transformations, introduced by Kodaira in the 1960s, and their role in creating elliptic surfaces with multiple fibers. Examine the importance of vector bundles on elliptic surfaces across various mathematical disciplines, including algebraic geometry, gauge theory, and mathematical physics. Gain insights into how specific vector bundles on elliptic surfaces are affected by logarithmic transformations, utilizing the perspective of o-minimal geometry. Learn about ongoing research and collaborative efforts in this field, including joint works with L. Katzarkov and E. Lupercio.