RESEARCH STATEMENT: AN EXTENDED VERSION

My main areas of interest are non-archimedean analytic geometry, algebraic ge-ometry and their interaction, which often involves formal or birational geometries and various desingularization and stable reduction problems. Loosely speaking, Raynaud’s approach interprets non-archimedean geometry as a kind of birational formal geometry (see [FK] for a popularization of this point of view). The analog of the non-archimedean analytic spaces in algebra-geometric world are Riemann-Zariski spaces, which were used by Zariski and Nagata for applications to birational geometry. In particular, there exist various connections and a strong similarity be-tween algebraic objects: schemes, blow ups, Riemann-Zariski spaces, and their topological (or adic) analogs: formal schemes, formal blow ups, non-archimedean analytic spaces. In some of my works I exploited these links to prove algebraic results using analytic geometry, and analytic results using algebraic geometry. Past research During my undergraduate studies I worked on few problems in graph theory, see joint works [GT1], [GT2], [GTUS]. I worked also on a problem in additive numbe