Four-Genus Bounds from the 10/8+4 Theorem

This course aims to teach participants how to derive four-ball genus bounds and calculate bounds for satellite knots using the 10/8+4 theorem. The course covers the knot slicing obstruction for knots in the three-sphere, the relationship between signature and second Betti number of a spin 4-manifold, and techniques to improve existing bounds. The teaching method involves explaining theoretical concepts and presenting joint work in progress with collaborators. This course is intended for individuals interested in gauge theory, low-dimensional topology, and knot theory.