Hugo Luiz Mariano

• II Brazilian Meeting in Category Theory, AO.R

• Abstract

  Real Algebraic Geometry is an active research area with connections and applications in various branches of Mathematics such as algebraic theory of quadratic forms, analytic geometry and optimization. This project intends to introduce the student to the main topics in the area, preparing him to get in touch with current research and starting his insertion in a research group on related to…

  Real Algebraic Geometry: an Introduction, BP.IC

• Abstract

  In this work, we will study Model Theory from a algebro-geometric approach, that is to say, we will search the literature for the historical use of techniques analogous to schemes in the context of Categorial Model Theory. Centrally, the project will cover Steve Breiner's Ph.D thesis and related articles. Aiming at this, we firstly intend to insert the student in the context of Categorica…

  Model theory inspired in modern algebraic geometry, BP.IC

• Abstract

  This master's project in mathematics has the aim of deepening the student's contact with algebraic geometry - already developed at the level of scientific initiation - through the study of motivic cohomology and A1-homotopy theory, which were introduced mainly by V. Voevodsky, F. Morel, S. Bloch, and A. Suslin. These areas formed the basis for the proofs of Milnor conjecture (Voevodsky, 1…

  Motivic cohomology and characterizations of the Bloch-Kato conjecture, BP.MS

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