CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation for the last research proposal) Birthplace: Brazil
Marcos Jardim graduated in Physics at the University of Campinas, obtained a Master's degree in Mathematics at the University of Campinas and a PhD in Mathematics from the University of Oxford, where he worked under the supervision of Simon Donaldson and Nigel Hitchin. He held post-doctoral positions at Yale University, University of Pennsylvania and University of Massachussets at Amherst; most recently, he has spent a sabbatical year at the University of Edinburgh in 2017. He is currently a Full Professor at the University of Campinas. His research concentrates on Gauge Theory and Algebraic Geometry, focusing on the study of vector bundles on algebraic varieties. He has published 36 papers on international journals, and supervised 13 masters and 10 PhD students, as well as 12 post-doctoral researchers. (Source: Lattes Curriculum)
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Gauge theory is the study of differential equations involving connections on vector bundles over manifolds using methods from differential geometry, algebraic geometry and geometric analysis. This is area of research emerged in the late 1970s, especially after works by Michael Atiyah, Nigel Hitchin and simon Donaldson, among others, as a mathematical model for classical field theory in ma…
Instanton bundles are a class of algebraic vector bundles, first introduced in mathematical physics as solutions of the Yang-Mills equation over compactified space-time, and later much studied in algebraic geometry. The main questions (irreducibility, smoothness) about the moduli space of instanton bundles on 3-dimensional projective space have been recently settled, but there are many op…
This project will have as main areas of study algebraic geometry, complex geometry and global theory of holomorphic foliations. Its main goals are: show results about the existence of residues and localization of characteristic classes for holomorphic Lie algebroids; a concise study of non-integrable distributions in complex projective spaces; a characterization of nilpotent and semista…
(Only some records are available in English at this moment)
This project seeks to establish the study of logarithmic sheaves T_à over complete intersection schemes V(Ã), which are algebraic varieties given as the zero-set of a regular sequence à = {f_1, . . . , f_k} of homogeneous polynomials in the projective space of dimension n. These sheaves are defined as the kernel of the Jacobian morphism J_à = (f_1, . . . , f_k), generalizing the classical…
Moduli theory has been a central theme in Algebraic Geometry. To construct moduli spaces, one usually needs the concept of stability conditions. Motivated by the work in string theory, Bridgeland introduced the stability conditions on a triangulated category and proposed the existence of a stability manifold. Moreover, there exists a locally finite wall and chamber structure on this manif…
In 2012 Bruzzo and Grassi proved a version of the Noether-Lefschetz Theorem for toric varieties, claiming that, on a very general quasi-smooth hypersurface X of an odd-dimensional projective simplicial toric Oda variety, with degree big enough, the (k,k)-cohomology classes of X come from the ambient space. The Noether-Lefschetz locus is the locus of quasi-smooth hypersurfaces with a fixed…
(Only some records are available in English at this moment)
The project has the aim to familiarize the student with the basic tools of algebraic topology through problems. To do that we will study the following problems: The relation between the fundamental group and the first homology group, fixed-point theorems, the Jordan Curve theorem and the Classification of Surfaces. (AU)
This project will cover aspects of the Mathematics of Solid Geometry, which deals with objects in three-dimensional Euclidean space. This project will especially focus on Polyhedra Classification, from the most usually taught in primary and higher education, to new classifications developed by the student and the supervisor. Basics concepts of Solid Geometry will be introduced with the go…
This project will consist in the study of Algebraic Varieties and Schemes with the intention of characterizing both objects and understanding the relationship between them. A special attention will be given to the schemes that cannot be represented with a variety structure, aiming to comprehend the advantages of the more modern definition compared to the classic one. During the course of …
(Only some records are available in English at this moment)
The main goal of this project is to give the beneficiary an opportunity to study with one of the leading researchers in Bridgeland stability, a topic in the state of the art within Algebraic Geometry that can relate to various other topics in both Algebraic Geometry and Physics. The idea is to study the stability properties of sheaves on P^3 with dimension 2 or less and how to translate …
The idea of this project consists in applying the tools of Bridgeland stability to moduli spaces of framed sheaves on Hirzebruch surfaces. In particular, three objectives are fixed: to study the chamber structure arising with the quiver description of Hilbert schemes of points of the total space of OP1(-n) (provided by the applicant in former works), to extend the already-mentioned quiver…
The study of moduli spaces of sheaves is a classical and relevant problem in algebraic geometry. The concept of stability is an important issue in this area, and the use of different notions can lead to a deeper understanding of the geometry of the moduli space of the object being studied.The present research project focuses on instanton sheaves on the 3 dimensional projective space. Thes…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 21 / 21 | Completed research grants |
| 5 / 5 | Ongoing scholarships in Brazil |
| 26 / 24 | Completed scholarships in Brazil |
| 7 / 7 | Completed scholarships abroad |
| 60 / 58 | All research grants and scholarships |
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