Related papers: Lectures on complements on log surfaces

We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.

Linear Geometry describes geometric properties that depend on the fundamental notion of a line. In this paper we survey basic notions and results of Linear Geomery that depend on the flat hulls: flats, exchange, rank, regularity,…

An algebraic technique adapted to the problems of the fundamental theoretical physics is presented. The exposition is an elaboration and an extension of the methods proposed in previous works by the aut

The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…

The subject of this paper is the problem of arrangement of a real nonsingular algebraic curve on a real non-singular algebraic surface. This paper contains new restrictions on this arrangement extending Rokhlin and Kharlamov-Gudkov-Krakhnov…

This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.

In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct interesting actions…

A brief survey of real algebraic structures on topological spaces is given. This article is written for the Gokova Gemetry/Topology Conference proceedings.

These lecture notes from a first course in algebraic topology use the fundamental group and orbit categories to classify covering spaces.

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…

These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were…

The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomology, Postnikov towers, the theory of "n-stuff", and…

This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which…

The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and…

These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

The paper is devoted to a generalized and improved version of author's approach to Gromov bounded cohomology theory. In particular, the awkward countability assumption is removed and the aspects related to homological algebra are clarified.…

These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in…