Related papers: The Abhyankar-Moh theorem for plane valuations at …

Clifford theory of possibly infinite dimensional modules is studied

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

We answer two questions about the topology of end spaces of infinite type surfaces and the action of the mapping class group that have appeared in the literature. First, we give examples of infinite type surfaces with end spaces that are…

We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.

In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.

We investigate two notions about descriptions of groups using first-order language: quasi-finite axiomatizability, concerning infinite groups, and polylogarithmic compressibility, concerning classes of finite groups.

We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…

A vanishing theorem is proved for Ext groups over non-commutative graded algebras. Along the way, an "infinite" version is proved of the non-commutative Auslander-Buchsbaum theorem.

We prove an analog of Gromov--Lawson type relative index theorems for K-homology classes.

Given a perfectoid field, we find an elementary extension and a henselian defectless valuation on it, whose value group is divisible and whose residue field is an elementary extension of the tilt. This specializes to the almost purity…

In this article, we present a complete classification, with normal forms, of the real algebraic curves under blow-spherical homeomorphisms at infinity.

In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.

We use group homology to define invariants in algebraic K-theory and in an analogue of the Bloch group for Q-rank one lattices and for some other geometric structures. We also show that the Bloch invariants of CR structures and of flag…

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.

We study group extensions of Finite Abelian Groups using matrices. We also prove a Theorem for equivalence of extensions using matrices.

We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems. The results are new even in the Euclidean setting.

Let $R$ be a complete equicharacteristic noetherian local domain and $\nu$ a valuation of its field of fractions whose valuation ring dominates $R$ with trivial residue field extension. The semigroup of values of $\nu$ on $R\setminus \{0\}$…

We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…

We develop class field theory of curves over $p$-adic fields which extends the unramified theory of S. Saito. The class groups which approximate abelian \'etale fundamental groups of such curves are introduced in the terms of algebraic…

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.