Related papers: A remark on virtual orientations for complete inte…

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…

Object goal navigation aims to navigate an agent to locations of a given object category in unseen environments. Classical methods explicitly build maps of environments and require extensive engineering while lacking semantic information…

We prove a new formula for the Hirzebruch-Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the…

We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical…

Scaling up visual category recognition to large numbers of classes remains challenging. A promising research direction is zero-shot learning, which does not require any training data to recognize new classes, but rather relies on some form…

We present an approach over arbitrary fields to bound the degree of intersection of families of varieties in terms of how these concentrate on algebraic sets of smaller codimension. This provides in particular a substantial extension of the…

In this short notice we give a universal definition of $\Z_2$-module $Or(\Gamma)$ of orientations of a graph $\Gamma$ and construct a method, by means of which one can easily verify whenever two such special definitions coincide.

A class theorem is presented and proved: the complex Fourier transforms of a certain class of exponential functions have all their zeros on the real line. A class of basis functions is first considered, and the class is then extended via…

The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.

We suggest a construction of virtual fundamental classes of certain types of moduli spaces.

Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…

We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally…

Leveraging class semantic descriptions and examples of known objects, zero-shot learning makes it possible to train a recognition model for an object class whose examples are not available. In this paper, we propose a novel zero-shot…

The motivation for this work is to construct a map from classical knots to virtual ones. What we get in the paper is a series of maps from knots in the full torus (thickened torus) to flat-virtual knots. We give definition of flat-virtual…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

Reference path following is a key component in the functioning of almost all engineered autonomous agents. Among several path following guidance methods in existing literature, vector-field-based guidance approach has got wide attention…

Some divisor class relations are proved and used to compute the Cartier divisor class of the virtual canonical bundle for genus 0 maps to a smooth target.

Let $X$ be a compact smooth manifold with boundary. In this article, we study the spaces $\mathcal V^\dagger(X)$ and $\mathcal V^\ddagger(X)$ of so called boundary generic and traversally generic vector fields on $X$ and the place they…

These notes aim to give an introduction to a few aspects of noncommutative geometry.