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.
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
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.
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