Related papers: On group-theoretic models of randomness and generi…

We examine the difference between several notions of curvature homogeneity and show that the notions introduced by Kowalski and Van\v{z}urov\'a are genuine generalizations of the ordinary notion of $k$-curvature homogeneity. The homothety…

We investigate conformal dimension for the class of infinite hyperbolic groups in the Gromov density model $\mathcal{G}^d_{m,l}$ of random groups with $m \geq 2$ fixed generators, density $0 < d < 1/2$ and relator length $l \to \infty$. Our…

A theorem of the Kolmogorov--Chentsov type is proved for random fields on a Riemannian manifold.

Following the construction from `Degrees of growth of finitely generated groups and the theory of invariant means' we generalize the Grigorchuk's overgroup $\tilde{\mathcal{G}}$, studied in `On parabolic subgroups and Hecke algebras of some…

We develop some basic homological theory of hopfological algebra as defined by Khovanov. Several homological properties in hopfological algebra analogous to those of usual homological theory of DG algebras are obtained.

In 2006 Z. Sela and independently O. Kharlampovich and A. Myasnikov gave a solution to the Tarski problems by showing that two non-abelian free groups have the same elementary theory. Subsequently Z. Sela generalized the techniques used in…

We describe an Aldous--Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the…

This note compares the usual (absolute) Gromov-Witten invariants of a symplectic manifold with the invariants that count the curves relative to a (symplectic) divisor D. We give explicit examples where these invariants differ even though it…

In this paper we look at which Alexander and Markov theories can be defined for generalized knot theories

In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range is large compare to genus. In fact, in such cases, we can…

We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding…

Let N be an o-minimal structure. In this paper we develop group extension and group cohomology theory over N and use it to describe the N-definable solvable groups. We prove an o-minimal analogue of the Lie-Kolchin-Mal'cev theorem and we…

We develop a formalism for relative Gromov-Witten invariants of Li that is analogous to the Symplectic Field Theory of Eliashberg, Givental, and Hofer. This formalism allows us to express natural degeneration formulae in terms of generating…

We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…

We lay the foundations for the study of relatively quasiconvex subgroups of relatively hyperbolic groups. These foundations require that we first work out a coherent theory of countable relatively hyperbolic groups (not necessarily finitely…

We generalize a class of groups defined by Rostislav Grigorchuk to a much larger class of groups, and provide upper and lower bounds for their word growth (they are all of intermediate growth) and period growth (under a small additional…

We discuss a very general Kirillov Theory for the representations of certain nilpotent groups which gives a combined view an many known examples from the literature.

We consider invariants of a finite group related to the number of random (independent, uniformly distributed) conjugacy classes which are required to generate it. These invariants are intuitively related to problems of Galois theory. We…

Gromov-Witten invariants for arbitrary projective varieties and arbitrary genus are constructed using the techniques from K. Behrend, B. Fantechi: The intrinsic normal cone.

We introduce a theoretical framework for performing statistical tasks---including, but not limited to, averaging and principal component analysis---on the space of (possibly asymmetric) matrices with arbitrary entries and sizes. This is…