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Explore advanced mathematical concepts through this comprehensive winter school lecture series covering categorification, representation theory, and symplectic geometry. Delve into four major topic areas through structured multi-part presentations: Eugene Gorsky's exploration of Hilbert schemes and their connections to knot homology, Yankı Lekili's examination of Fukaya categories and their applications in representation theory, Andrew Mathas's detailed treatment of cyclotomic KLR algebras, and Volodymyr Mazorchuk's introduction to 2-representation theory. Master the intricate relationships between algebraic geometry, topology, and representation theory as presented by leading experts in the field. Gain insights into cutting-edge research areas including the geometric and categorical approaches to knot invariants, symplectic geometry's role in representation theory, and the algebraic structures underlying these mathematical frameworks. Access lectures delivered at the prestigious Hausdorff Research Institute for Mathematics, providing rigorous mathematical exposition suitable for graduate students and researchers working in algebra, geometry, and topology.
