Related papers: Stratification and the smashing spectrum
In several familiar subcategories of the category ${\mathbb T}$ of topological spaces and continuous maps, embeddings are not pushout-stable. But, an interesting feature, capturable in many categories, namely in categories $\mathcal{B}$ of…
One point compactification is studied in the light of ideal of subsets of $\mathbb{N}$. $\mathcal{I}$-proper map is introduced and showed that a continuous map can be extended continuously to the one point $\mathcal{I}$-compactification if…
Monadic stability generalizes many tameness notions from structural graph theory such as planarity, bounded degree, bounded tree-width, and nowhere density. The sparsification conjecture predicts that the (possibly dense) monadically stable…
A four-dimensional universe, arising from a flux compactification of Type IIB string theory, contains scalar fields with a potential determined by topological and geometric parameters of the internal -hidden- dimensions. We show that…
We investigate from an algebraic and topological point of view the minimal prime spectrum of a universal algebra, considering the prime congruences w.r.t. the term condition commutator. Then we use the topological structure of the minimal…
Finite tensor categories (FTCs) $\bf T$ are important generalizations of the categories of finite dimensional modules of finite dimensional Hopf algebras, which play a key role in many areas of mathematics and mathematical physics. There…
I review the arguments in favor of/against the traditional hypothesis that the Planck, string and compactification scales are all within a couple of orders of magnitude from each other. I explain how the extreme brane-world scenario, with…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
Given a suitable stable monoidal model category $\mathscr{C}$ and a specialization closed subset $V$ of its Balmer spectrum one can produce a Tate square for decomposing objects into the part supported over $V$ and the part supported over…
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…
We give the site-theoretic account of the spectral construction as first introduced by Coste. We provide a detailed examination of the geometric properties of the spectrum, in particular what classes of topoi it produces when applied to the…
The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…
For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…
We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of…
The recent measurements of cosmological parameters by the Planck collaboration favors inflationary models with a redshifted spectrum and a very low tensor-to-scalar ratio. Two well-studied scenarios in the particle physics/string theory…
We find the sharp bounds on $h^0(F)$ for one-dimensional semistable sheaves $F$ on a projective variety $X$ by using the spectrum of semistable sheaves. The result generalizes the Clifford theorem. When $X$ is the projective plane…
We conjecture that for a strongly minimal theory T in a finite signature satisfying the Zilber Trichotomy, there are only three possibilities for the recursive spectrum of T: all countable models of T are recursively presentable; none of…
We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…
By virtue of Balmer's celebrated theorem, the classification of thick tensor ideals of a tensor triangulated category $\T$ is equivalent to the topological structure of its Balmer spectrum $\spc \T$. Motivated by this theorem, we discuss…
In classification problems, sampling bias between training data and testing data is critical to the ranking performance of classification scores. Such bias can be both unintentionally introduced by data collection and intentionally…