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I will survey various results on applications and extensions of Hofer-Wysocki-Zehnder's polyfold theory: - fiber products of polyfold Fredholm sections - equivariant transversality - existence and obstructions - equivariant fundamental class -

We develop a continuous version of Kasteleyn theory to show that partition functions for bead configurations on T_n may be expressed in terms of Fredholm determinants of certain operators on

dress an important and challenging set of problems: computation of Fredholm and Volterra. ... been already noted in the computation of spectra of Fredholm operators. •

Consider a space XX, such as a compact space of JJ-holomorphic stable maps with closed domain, that is the zero set of a Fredholm operator.

D. T.-R. McLaughlin, and A. Minakov. Soliton v.the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kineticequation arXiv:2205.02601, 2022.