Related papers: Algebraic Gromov ellipticity: a brief survey
We study some homological invariants of a given generalized bound path algebra in terms of those of the algebras used in its construction. We discuss the particular case where the algebra is a generalized path algebra and give conditions…
We apply classical invariant theory of binary forms to explicitly characterize isomorphism classes of hyperelliptic curves of small genus and, conversely, propose algorithms for reconstructing hyperelliptic models from given invariants. We…
This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active…
We survey new results on finite groups of birational transformations of algebraic varieties.
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
We present a simple and efficient algorithm to compute the sum of the algebraic conjugates of a point on an elliptic curve.
We give a geometric characterization of extremal sets in ell_p spaces that generalizes our previous result for such sets in Hilbert spaces.
Relative orbifold Gromov-Witten theory is set-up and the degeneration formula is given.
In these lecture notes I give an elementary introduction to elliptic hypergeometric functions. I focus on motivating the main ideas and constructions, rather than giving a comprehensive survey. The lectures include a brief explanation of…
In this revised version, we add some expository material and references and make some minor corrections.
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
Fix a prime number $p$. We report on some recent developments in algebraic geometry (broadly construed) over $p$-adically complete commutative rings. These developments include foundational advances within the subject as well as external…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
For smooth projective G-varieties, we equate the gauged Gromov-Witten invariants for sufficiently small area and genus zero with the invariant part of equivariant Gromov-Witten invariants. As an application we deduce a gauged version of…
We establish a quantitative version of the Gromov compactness theorem for closed genus 0 pseudoholomorphic curves in the setting of a tamed almost complex manifold with bounded geometry.
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
We present a complete classification of complex plane algebraic curves, equipped with the induced Euclidean, up to global bilipschitz homeomorphism.
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
This is an overview of some of the invariants that were discovered by Welschinger in the context of enumerative real algebraic geometry. Their definition finds a natural setup in real symplectic geometry. In particular, they can be studied…