Related papers: Modular forms for chromatic homotopy: Supersingula…
We establish a hidden extension in the Adams spectral sequence converging to the stable homotopy groups of spheres at the prime 2 in the 54-stem. This extension is exceptional in that the only proof we know proceeds via Pstragowski's…
We prove many simultaneous congruences mod 2 for elliptic and Hilbert modular forms among forms with different Atkin--Lehner eigenvalues. The proofs involve the notion of quaternionic $S$-ideal classes and the distribution of Atkin--Lehner…
We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while $\theta_{13} = 0$ and the solar mixing angle $\theta_{12}$ remains undetermined; without finetuning, $\theta_{12}$ will be large but…
This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential…
We identify an overlooked Wess--Zumino--Witten structure in the hidden-local-symmetry~(HLS) formulation of vector mesons. The newly identified term generically leads to the topological quantization of the vector-meson anomalous couplings.…
Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry classes are identified, which correspond to Cartan's…
We prove a version of the weight part of Serre's conjecture for mod $p$ Galois representations attached to automorphic forms on rank 2 unitary groups which are non-split at $p$. More precisely, let $F/F^+$ denote a CM extension of a totally…
We study the irregularity sheaves attached to the $A$-hypergeometric $D$-module $M_A(\beta)$ introduced by Gel'fand et al., where $A\in\mathbb{Z}^{d\times n}$ is pointed of full rank and $\beta\in\mathbb{C}^d$. More precisely, we…
We prove several supercongruences involving the harmonic number of order two $H_n^{(2)}:=\sum_{k=1}^n1/k^2$. For example, if $p>5$ is prime and $\alpha$ is $p$-integral, then we can completely determine $$…
We establish well-posedness theory for the 1D mass-subcritical nonlinear Schr\"odinger equation (NLS) having power-type nonlinearity $|u|^{\alpha-1}u$ in a certain modulation spaces $M^{p,p'}(\mathbb{R}),$ where $p'$ is a H\"older conjugate…
Composite vector resonances in the triplet of the SM SU$(2)_{L}$ gauge group are a universal prediction of "natural" new physics models involving a new strongly-interacting sector and are therefore among the most plausible new particles…
We use the newly developed technique of inverse quantum hamiltonian reduction to investigate the representation theory of the simple affine vertex algebra $\mathsf{A}_{2}(\mathsf{u},2)$ associated to $\mathfrak{sl}_{3}$ at level $\mathsf{k}…
We develop the theory and algorithms necessary to be able to verify the strong Birch--Swinnerton-Dyer Conjecture for absolutely simple modular abelian varieties over $\mathbf{Q}$. We apply our methods to all 28 Atkin--Lehner quotients of…
Supersymmetry is one of the most plausible extensions of the Standard Model, since it is well motivated by the hierarchy problem, supported by measurements of the gauge coupling strengths, consistent with the suggestion from precision…
We present a conjecture for the leading $1/N$ anomalous dimension of the scalar primary operator in $U(N)_k$ Chern-Simons theories coupled to a single fundamental field, to all orders in the t'Hooft coupling $\lambda=\frac{N}{k}$. Following…
A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…
This paper completes the proof of the Ramanujan Conjecture for holomorphic Hilbert modular forms whose weights are all congruent modulo 2. As a consequence, the Weight-Monodromy Conjecture and the zeta function conjecture of Langlands are…
We present the complete set of continuous maximal symmetries that the potential of an $n$-Higgs Doublet Model ($n$HDM) should satisfy for natural Standard Model (SM) alignment. As a result, no large mass scales or fine-tuning is required…
In this paper, we explore a two-way connection between quasimodular forms of depth $1$ and a class of second-order modular differential equations with regular singularities on the upper half-plane and the cusps. Here we consider the cases…
We study the moduli space of a super Chern-Simons theory on a manifold with the topology ${\bf R}\times \S$, where $\S$ is a compact surface. The moduli space is that of flat super connections modulo gauge transformations on $\S$, and we…