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Explore a conference talk delving into advanced topics in gauge theory and low-dimensional topology. Learn about new four-genus bounds derived from the 10/8+4 theorem, expanding on Donald and Vafaee's knot slicing obstruction. Discover how this technique relates the signature and second Betti number of spin 4-manifolds with boundaries of zero-surgery on knots. Gain insights into the application of these methods to obtain four-ball genus bounds and their computation for satellite knots. Understand the connections between Furuta's 10/8 theorem and the improved 10/8+4 theorem by Hopkins, Lin, Shi, and Xu. Follow the ongoing research conducted jointly with Sashka Kjuchukova and Gordana Matic, presented by Linh Truong from the University of Michigan at the Gauge Theory and Low Dimensional Topology conference held at the University of Miami.
