In this paper we study the $\mathbb{C}^*$-fixed points in moduli spaces of Higgs bundles over a compact Riemann surface for a complex semisimple Lie group and its real forms. These fixed points are called Hodge bundles and correspond to complex varia...
We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases....
The double ramification (DR) cycle associated to a line bundle on a family of curves detects where the line bundle becomes fibrewise-trivial. The Hodge-DR Conjecture proposes a formula for powers of the first Chern class of a natural line bundle on t...
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A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of $G$-zips of connected-Hodge-type; such schemes should include all Hodge-typ...
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern...
In these notes, we introduce various approaches (GIT, Hodge theory, and KSBA) to constructing and compactifying moduli spaces. We then discuss the pros and cons for each approach, as well as some connections between them....
We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived Torelli The...
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Hodge/Bochner Laplacians of simplicial complexes, their spectra, higher-order diffusion and random walks (⭐ 32)
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The natural Helmholtz-Hodge decomposition (⭐ 33)
Did the Siege Perilous get rid of the X-Men’s ability to be invisible on digital media? If so, is there any one who was resurrected that didn’t go through the Siege and should still be invisible? ...
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This paper reports on a survey of star clusters in M31 based on archival images from the Hubble Space Telescope. Paper I (Krienke and Hodge 2007) reported results from images obtained with the Wide Field/Planetary Camera 2 (WFPC2) and this paper re...
Francis – WG Tyler Gardiner – HK Alex Gerrard – PR Jack Hickson – FE Jayden Hodges – HK Kellen Jenner – CE Marcus Jensen – CE, WG Sam Johnstone – PR Jordan