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Lam, Lee and Shimozono recently introduced backstable double Grothendieck polynomials to represent $K$-theory classes of the infinite flag variety. They used them to define double $\beta$-Stanley symmetric functions, which expand into…

Kim, K\"uhn, Osthus and Tyomkyn (Trans. Amer. Math. Soc. 371 (2019), 4655--4742) greatly extended the well-known blow-up lemma of Koml\'os, S\'ark\"ozy and Szemer\'edi by proving a `blow-up lemma for approximate decompositions' which states…

This paper presents a topological framework for investigating the Birch and Swinnerton Dyer conjecture through four dimensional embeddings of elliptic curves. We propose a correspondence between the algebraic rank of an elliptic curve and…

We begin with a new analysis of formal words. Let w be a formal word in letters g_1,...,g_k. The word map associated with w maps the permutations s_1,...,s_k in S_n to the permutation obtained by replacing for each i, every occurrence of…

This paper is essentially made of the three preprints arXiv:1212.5818, arXiv:1311.0187, arXiv:1603.07876 gathered in a single text, with simplified proofs. We recall several results of the microlocal theory of sheaves of Kashiwara-Schapira…

Bleher et al. began studying higher codimension Iwasawa theory for classical Iwasawa modules. Subsequently, Lei and Palvannan studied an analogue for elliptic curves with supersingular reduction. In this paper, we obtain a vast…

The extension of the linear flavor-wave theory (LFWT) to fully antisymmetric irreducible representations (irreps) of $\mathrm{SU}(N)$ is presented in order to investigate the color order of $\mathrm{SU}(N)$ antiferromagnetic Heisenberg…

In this note it is shown that if $\mu$ is an $n$-Ahlfors regular measure in $\mathbb R^{n+1}$ such that the $n$-dimensional Riesz transform is bounded in $L^2(\mu)$ and the so-called BAUPP (bilateral approximation by unions of parallel…

Until recently, most experts would probably have agreed we cannot backwards-step in constant time with a run-length compressed Burrows-Wheeler Transform (RLBWT), since doing so relies on rank queries on sparse bitvectors and those inherit…

A \emph{metric tree embedding} of expected \emph{stretch~$\alpha \geq 1$} maps a weighted $n$-node graph $G = (V, E, \omega)$ to a weighted tree $T = (V_T, E_T, \omega_T)$ with $V \subseteq V_T$ such that, for all $v,w \in V$,…

We study the approximation of functions that map a Euclidean domain $\Omega\subset \mathbb{R}^{d}$ into an $n$-dimensional Riemannian manifold $(M,g)$ minimizing an elliptic, semilinear energy in a function set $H\subset W^{1,2}(\Omega,M)$.…

We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for $A_{\infty }$. The covariant string field splits into the light-cone string field and trivial…

A Sidorenko bigraph is one whose density in a bigraphon $W$ is minimized precisely when $W$ is constant. Several techniques of the literature to prove the Sidorenko property consist of decomposing (typically in a tree decomposition) the…

While research on the geometry of planar graphs has been active in the past decades, many properties of planar metrics remain mysterious. This paper studies a fundamental aspect of the planar graph geometry: covering planar metrics by a…

K -> Pi Pi decays are investigated in the framework of the SU(2)left x U(1) gauge theory of J=0 mesons proposed in ref.[1], to which is added an interaction between mesons respecting the two symmetries generally attributed to strong…

We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

The affine Grassmannian of $SL_n$ admits an embedding into the Sato Grassmannian, which further admits a Pl\"ucker embedding into the projectivization of Fermion Fock space. Kreiman, Lakshmibai, Magyar, and Weyman describe the linear part…

We construct equivariant, string and leading order characteristic classes and Chern-Simons classes for certain infinite rank bundles associated to fibrations occurring in loop spaces, Gromov-Witten theory and gauge theory. Results include a…

We give a new Littlewood-Richardson rule for the Schubert structure coefficients of isotropic Grassmannians, equivalently for the multiplication of $P$-Schur functions. Serrano (2010) previously gave a formula in terms of classes in his…