Frontiers in Geometry and Topology: (Proceedings of Symposia in Pure Mathematics)

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.

Table of Contents:
Articles Francesco Lin, Lectures on families of Dirac operators and applications Thomas Walpuski, Lectures on generalised Seiberg-Witten equations Nima Anvari, A splitting formula in instanton Floer homology Nima Anvari and Ian Hambleton, Finite group actions on $4$-manifolds and equivariant bundles Dave Auckly and Daniel Ruberman, Exotic families of embeddings John A. Baldwin and Steven Sivek, An instanton take on some knot detection results Hans U. Boden, Christopher M. Herald and Paul Kirk, Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott Lothar Gottsche, Blowup formulas for Segre and Verlinde numbers of surfaces and higher rank Donaldson invariants Kristen Hendricks, Jennifer Hom, Matthew Stoffregen and Ian Zemke, A note on PL-disks and rationally slice knots Robert Lipshitz and Sucharit Sarkar, Khovanov homology of strongly invertible knots and their quotients Paolo Lisca and Andrea Parma, On almost complex embeddings of rational homology balls Maggie Miller, Explicitly describing fibered 3-manifolds through families of singularly fibered surfaces Andras I. Stipsicz and Zoltan Szabo, On the minimal genus problem in four-manifolds Joshua Wang, The Gysin sequence and the $\mathfrak {sl}(N)$ homology of $T(2,m)$ Claudius Zibrowius, Heegaard Floer multicurves of double tangles

About the Author :
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.