The Bloch--Kato conjecture predicts that the dimension of the Selmer group of a global Galois representation is equal to the order of vanishing of its L-function. In this talk, I...
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Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity, striking a balance between simpler models that exhibit high...
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The Thouless-Anderson-Palmer (TAP) approach to the Sherrington-Kirkpatrick mean field spin glass model was proposed in one of the earliest papers on this model. Since then it has complemented subsequently elaborated...
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Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical...
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Quiver theory and machine learning share a common ground, namely, they both concern about linear representations of directed graphs. The main difference arises from the crucial use of non-linearity in...
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Using recent advances in the Minimal Model Program for moduli spaces of sheaves on the projective plane, we compute the cohomology of the tensor product of general semistable bundles on...
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I shall report on a new approach to study some classes of quantum circuits and exactly solvable models. Concretely, using knots gives a unified framework to characterize two famous classes...
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Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to...
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Graph representation learning has emerged as a dominant paradigm for networked data. Still, prevailing methods require abundant label information and focus on representations of nodes, edges, or entire graphs. While...
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Mazur conjectured, after Faltings’s proof of the Mordell conjecture, that the number of rational points on a curve of genus g at least 2 defined over a number field of...
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