相关论文: Harder-Narasimhan Filtrations and Zigzag Persisten…
Symmetric quiver varieties with potentials are natural generalizations of Nakajima quiver varieties, and their equivariant critical cohomologies provide more flexible settings for geometric representation theory and enumerative geometry. In…
We continue the research of the relation $\hspace{1mm}\widetilde{\mid}\hspace{1mm}$ on the set $\beta {\mathbb{N}}$ of ultrafilters on ${\mathbb{N}}$, defined as an extension of the divisibility relation. It is a quasiorder, so we see it as…
The $\gamma$-linear projected barcode was recently introduced as an alternative to the well-known fibered barcode for multiparameter persistence, in which restrictions of the modules to lines are replaced by pushforwards of the modules…
There is a bijection between odd prime dimensional qudit pure stabilizer states modulo invertible scalars and affine Lagrangian subspaces of finite dimensional symplectic $\mathbb{F}_p$-vector spaces. In the language of the stabilizer…
Let $X$ be a Hirzebruch surface, and let $H$ be any ample divisor. In this paper, we algorithmically determine when the moduli space of semistable sheaves $M_{X,H}(r,c_1,c_2)$ is nonempty. Our algorithm relies on certain stacks of…
For a family of principal bundles with a reductive structure group on a family of curves in characteristic zero, it is known that the Harder Narasimhan type of its restriction to each fiber varies semicontinuously over the parameter scheme…
The short-time stability of concentration profiles in coherent periodic multilayers consisting of two components with large miscibility gap is investigated by analysing stationary solutions of the Cahn-Hilliard diffusion equation. The…
We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or…
We consider a notion of stability for sheaves, which we call multi-Gieseker stability that depends on several ample polarisations $L_1, \dots, L_N$ and on an additional parameter $\sigma \in \mathbb{Q}_{\geq 0}^N\setminus\{0\}$. The set of…
In this paper we consider a class of fully nonlinear forced and reversible Schroedinger equations and prove existence and stability of quasi-periodic solutions. We use a Nash-Moser algorithm together with a reducibility theorem on the…
We present a novel comprehensive first-principles theoretical study of the electronic properties and relative stabilities of edge-oxidized zigzag graphene nanoribbons. The oxidation schemes considered include hydroxyl, carboxyl, ether, and…
We bound the generation level of the Hodge filtration on the localization along a hypersurface in terms of its minimal exponent. As a consequence, we obtain a local vanishing theorem for sheaves of forms with log poles. These results are…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to…
Calabi-Yau Fermat varieties are obtained from moduli spaces of Lagrangian connect sums of graded Lagrangian vanishing cycles on stability conditions on Fukaya-Seidel categories. These graded Lagrangian vanishing cycles are stable…
We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.
Persistence modules have a natural home in the setting of stratified spaces and constructible cosheaves. In this article, we first give explicit constructible cosheaves for common data-motivated persistence modules, namely, for modules that…
Our objective in this article is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of the (say) simplicial set embedded in a finite dimensional vector space…
Computing persistence over changing filtrations give rise to a stack of 2D persistence diagrams where the birth-death points are connected by the so-called `vines'. We consider computing these vines over changing filtrations for zigzag…
We compute the Harder-Narasimhan filtration of vector bundles $f_*\mathcal O_Y$ for certain finite morphisms $f\,:\,Y\,\longrightarrow\, X$ and in some other cases.