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This volume contains the proceedings of the summer school and research conference ""Frontiers in Geometry and Topology"", celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1-12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP).The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology.Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
Paul M. N. Feehan, Rutgers, The State University of New Jersey, Piscataway, NJ, Lenhard L. Ng, Duke University, Durham, NC, and Peter S. Ozsvath, Princeton University, NJ.
ArticlesFrancesco Lin, Lectures on families of Dirac operators and applicationsThomas Walpuski, Lectures on generalised Seiberg-Witten equationsNima Anvari, A splitting formula in instanton Floer homologyNima Anvari and Ian Hambleton, Finite group actions on $4$-manifolds and equivariant bundlesDave Auckly and Daniel Ruberman, Exotic families of embeddingsJohn A. Baldwin and Steven Sivek, An instanton take on some knot detection resultsHans U. Boden, Christopher M. Herald and Paul Kirk, Examples of homology 3-spheres whose Chern-Simons function is not Morse-BottLothar Gottsche, Blowup formulas for Segre and Verlinde numbers of surfaces and higher rank Donaldson invariantsKristen Hendricks, Jennifer Hom, Matthew Stoffregen and Ian Zemke, A note on PL-disks and rationally slice knotsRobert Lipshitz and Sucharit Sarkar, Khovanov homology of strongly invertible knots and their quotientsPaolo Lisca and Andrea Parma, On almost complex embeddings of rational homology ballsMaggie Miller, Explicitly describing fibered 3-manifolds through families of singularly fibered surfacesAndras I. Stipsicz and Zoltan Szabo, On the minimal genus problem in four-manifoldsJoshua Wang, The Gysin sequence and the $\mathfrak {sl}(N)$ homology of $T(2,m)$Claudius Zibrowius, Heegaard Floer multicurves of double tangles
