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Explore the concept of rational slice genus in knot theory through a conference talk delivered at the Gauge Theory and Low Dimensional Topology event. Delve into the use of relative adjunction inequalities for properly embedded surfaces in smooth 4-manifolds to investigate the rational slice genus of knots in a rational homology sphere. Learn how this 4-dimensional analogue of the rational Seifert genus, introduced by Calegari and Gordon, presents unique challenges in computation. Discover surprising results in determining the rational slice genus for certain classes, including Floer simple knots, despite the complexity of solving an infinite number of minimal genus problems. Gain insights into joint work with Katherine Raoux, presented by Matt Hedden from Michigan State University, in this hour-long lecture that bridges gauge theory and low-dimensional topology.
