## Topology Seminar (Main Talk): Where do Seiberg-Witten equations come from?

Seminar | August 22 | 4-5 p.m. | 3 Evans Hall

Selman Akbulut, Michigan State University

Department of Mathematics

The question in the title is akin to asking where the equation of motion of a free falling object $a + bt + 1/2 gt^2$ in 3-space come from? then discovering that the "objects fall with constant acceleration" rule. Similarly, we derive Seiberg-Witten equations (which also have a linear part and a quadratic part) from the deformation equations of an "isotropic associative submanifold" of a complex $G_2$ Manifold. For this, we will define the notion of complex $G_2$ manifold and notion of complexification of a $G_2$ manifold (this is a joint work with Ustun Yildirim).

c_abbott@berkeley.edu