Related papers: Algebraic Gromov ellipticity: a brief survey
We establish the equivalence of Gromov ellipticity and subellipticity in the algebraic category.
This is a survey of results on the Hilbert property of algebraic varieties, and variants of it.
We construct examples of nodal quartic double solids that admit uniformly rational, and so elliptic in Gromov' sense, small algebraic resolutions.
We prove that every nontrivial principal $G_m$-bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
This is a survey paper on Alegbraic Geometry over Lie Algebras
We show that every smooth cubic hypersurface X in P^{n+1}, n> 1 is algebraically elliptic in Gromov's sense. This gives the first examples of non-rational projective manifolds elliptic in Gromov's sense. We also deduce that the punctured…
A short survey on applications of algebraic geometry in topological data analysis.
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the…
We present two explicit recursions which determine the elliptic Gromov-Witten invariants of CP^3 in terms of the rational ones, and give a table up to degree 5. Unlike the rational Gromov-Witten invariants, the coefficients are negative and…
We find classes of projective manifolds that are elliptic in the sense of Gromov and such that the affine cones over these manifolds also are elliptic off their vertices. For example, the latter holds for any generalized flag manifold of…
The paper consists of two parts. The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results. It may be regarded as a brief exposition of some ideas from the book in progress:…
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.
Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
This is a survey talk on the study of Gel'fand-Dorfman bialgebras.
We discuss the basic properties of various versions of two variable elliptic genus with special attention to the equivariant elliptic genus. The main applications are to the elliptic genera attached to non-compact GITs, including the…