Related papers: Bernstein-Sato Varieties and Annihilation of Power…

Let $S$ be a commutative noetherian ring. The extensions of matrix factorizations of non-zerodivisors $x_1,\dots,x_n$ of $S$ form a full subcategory of finitely generated modules over the quotient ring $S/(x_1\cdots x_n)$. In this paper, we…

Generalizing work of Smith and Hara, we give a new characterization of log-terminal singularities for finitely generated algebras over $\mathbb C$, in terms of purity properties of ultraproducts of characteristic $p$ Frobenii. The first…

Given a finite index subfactor, we show that the {\em affine morphisms at zero level} in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a *-algebra. This…

This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite…

Let $G$ be a split reductive group over a field $k$ of arbitrary characteristic, chosen suitably. Let $X\to S$ be a smooth projective morphism of locally noetherian $k$-schemes, with geometrically connected fibers. We show that for each…

The computation of the cohomology for finite groups of Lie type in the describing characteristic is a challenging and difficult problem. In earlier work, the authors constructed an induction functor which takes modules over the finite group…

We use Drinfeld's relative compactifications and the Tannakian viewpoint on principal bundles to construct the Harder-Narasimhan stratification of the moduli stack Bun_G of G-bundles on an algebraic curve in arbitrary characteristic,…

We study holomorphic germs $f:(\mathbb{C}^2, 0) \rightarrow (\mathbb{C}^2,0) with non-invertible differential $df_0$. In order to do this, we search for a modification $\pi:X \rightarrow (\mathbb{C}^2,0)$ (i.e., a composition of point…

In this paper we prove that the Bernstein-Sato polynomial of any free divisor for which the $D[s]$-module $D[s] h^s$ admits a Spencer logarithmic resolution satisfies the symmetry property $b(-s-2) = \pm b(s)$. This applies in particular to…

For a ribbon fusion category $\mathcal{A}$ and a special symmetric commutative Frobenius algebra $F$ in $\mathcal{A}$, we use factorization homology and the ansular correlators obtained via the modular microcosm principle to construct a…

This paper studies the relationship between the nuclear norm-regularized minimization problem, which minimizes the sum of a $C^2$ function $h$ and a positive multiple of the nuclear norm, denoted by $f$, and its factorized problem obtained…

The algebraic extension $\boldsymbol{B}_{\mathbb{Z}}^{\mathscr{F}}$ of the extended bicyclic semigroup for an arbitrary $\omega$-closed family $\mathscr{F}$ subsets of $\omega$ is introduced. It is proven that…

Let $\textbf{H} = ((H, F^{\bullet}), L)$ be a polarized variation of Hodge structure on a smooth quasi-projective variety $U.$ By M. Saito's theory of mixed Hodge modules, the variation of Hodge structure $\textbf{H}$ can be viewed as a…

Let $f:\mathcal{X}\to S$ be a proper holomorphic submersion of complex manifolds and $G$ a complex reductive linear algebraic group with Lie algebra $\mathfrak{g}$. Assume also given a holomorphic principal $G$-bundle $\mathcal{P}$ over…

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U(N_c) gauge theory with N_f<N_c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli,…

We consider the possible disentanglements of holomorphic map germs $f \colon (\mathbb C^n,0) \to (\mathbb C^N,0)$, $n < N$, with nonisolated locus of instability $\operatorname{Inst}(f)$. The aim is to achieve lower bounds for their…

Fix a commutative monoid $(T,+,0)$, a commutative monoid $(\Gamma,+,0_\Gamma)$, and a map \[ (a,\alpha,b,\beta,c)\longmapsto a\,\alpha\,b\,\beta\,c\in T \] which is additive in each variable and associative in the ternary sense. A left…

The study of vector-like spectra in 4-dimensional F-theory compactifications involves root bundles, which are important for understanding the Quadrillion F-theory Standard Models (F-theory QSMs) and their potential implications in physics.…

Let $G$ be a finite group and $\mathsf{k}$ a field of characteristic $p$. It is conjectured in a paper of the first author and John Greenlees that the thick subcategory of the stable module category StMod$(\mathsf{k}G)$ consisting of…

Let $(X,\bullet )$ be a groupoid (binary algebra) and $Bin(X\dot{)}$ denote the collection of all groupoids defined on $X$. We introduce two methods of factorization for this binary system under the binary groupoid product \textquotedblleft…