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PubblicazioneLittlewood's estimates for L‐functions in the hyperelliptic ensemble( 2026)We investigate the analogs of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet (Formula presented.) -functions over function fields. In some situations, we are actually able to establish finer results in the function field setup than what is currently known in the original number field setup, and this leads us to an educated guess on what could happen for the Riemann zeta-function in such situations. Fourier analysis techniques play an important role in our approach.
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PubblicazioneFirst-principles real-space embedding theory of the superconducting proximity effect( 2026)When a superconductor is placed in contact with a normal material, Cooper pairs penetrate the latter and induce superconductivity via the proximity effect. Despite its central role in quantum materials, superconducting devices, and topological platforms, a predictive first-principles description of the proximity effect at realistic interfaces has remained computationally prohibitive so far. Here, we fill this gap by developing a Green's-function framework based on real-space dynamical embedding that enables first-principles simulations of superconducting proximity in mesoscopic systems. We show that the proximity effect admits a transparent diagrammatic formulation in terms of normal and anomalous embedding self-energies, which disentangle and quantify the distinct renormalization mechanisms generated by coupling to a superconducting bath. By combining this formalism with recursive schemes, we compute local spectral functions and proximity lengths extending over hundreds of nanometers into the bulk without resorting to thick interface slabs. We deploy the approach on tight-binding models (Qi-Hughes-Zhang and Fu-Kane-Mele), where we analyze mixed-parity superconductivity in topological insulators proximitized by s-wave superconductors, and on first-principles simulations of NbSe2/CrBr3 heterostructures based on density-functional theory and maximally localized Wannier functions, the latter enabling direct comparison with scanning tunneling spectroscopy experiments. Our work provides a scalable and conceptually unified framework that bridges microscopic electronic structure and mesoscale proximity physics, enabling predictive atomistic simulations of superconducting interfaces.
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PubblicazioneConfinement in a finite duality cascade( 2026)We provide several consistency checks of confining dynamics in a recently conjectured holographic dual of a four-dimensional N = 1 supersymmetric gauge theory that flows from a conformal manifold in the UV to a finite set of isolated, fully gapped vacua in the IR. This is obtained by considering D3-branes at the conifold singularity in the presence of an O7-plane, leading to a background where all supergravity fields have a non-trivial profile. We compute holographically the expectation value of a Wilson loop in the fundamental representation and show that it obeys an area law. We then construct the domain walls which interpolate between different vacua in terms of D5-branes wrapping a compact three-cycle of the internal manifold. Their dynamics is governed by the (2+1)-dimensional N = 1 Yang-Mills-Chern-Simons theory predicted by field theory arguments, that reduces in the deep infrared to a TQFT whose inflow action correctly reproduces the mixed anomaly of the four-dimensional theory. Finally, we argue that, unlike in previous models in the literature, axionic strings are unstable in this background. This implies that the corresponding massless axion that would couple to them is absent, in agreement with the fact that the vacua are fully gapped.
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PubblicazioneMaximizers of the L2 → L4 Fourier extension inequality for cones in finite fields( 2026)Sharp Fourier restriction inequalities in euclidean spaces and the restriction phenomenon in finite fields have both been topics of interest in the last few decades. Very recently, the research at the intersection of these two topics began. In [8], it was established that, for the (3,1)[jls-end-space/]-cone Γ(3,1)3:={η∈Fq4∖{0}:η12+η22+η32=η42}[jls-end-space/], the L2→L4 Fourier extension inequality is saturated by constant functions when (Formula presented). In this manuscript, we advance this line of inquiry by establishing sharp forms of L2→L4 Fourier extension inequalities for all the remaining cones Γ3⊂Fq4[jls-end-space/]. These cones include the (2,2)[jls-end-space/]-cone Γ(2,2)3:={η∈Fq4∖{0}:η12+η22=η32+η42} for general q=pn and the (3,1)[jls-end-space/]-cone when (Formula presented). Moreover, we classify all the extremizers in both cases. We note that the corresponding problem for the (2,2)[jls-end-space/]-cone in the euclidean setting remains open.
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PubblicazioneBubbles in AdS( 2026)We investigate loop corrections to the four-point function of identical scalar operators in a four-dimensional large N conformal field theory, holographically dual to AdS with a quartic interaction. We focus on the universal part of the correlator that, at any order in 1/N, is completely determined by tree-level data. We show how this contribution controls the part of the anomalous dimensions of double-trace operators, that exhibits a characteristic log l dependence at large spin l. We resum these effects to all orders in 1/N and show that they admit a natural effective description in AdS. Finally, by reformulating the problem in Mellin space, we demonstrate that the same contribution corresponds to consecutive unitarity cuts of bubble diagrams in the flat-space limit.