CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from 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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We present here the plan of activities for Prof. Renato Vidal Martins' visit to IMECC-UNICAMP. This project is based on an extensive research plan with two central themes, namely, Perverse Instanton Sheaves and Bridgeland Stability, as well as, Clifford Index of Torsion-Free Sheaves, both to be developed with Prof. Marcos Jardim. The first concerns the restructuring and generalization of …
This project stands at the crossroads of complex algebraic geometry and Riemannian geometry to put together a team of Brazilian and French experts from both disciplines with a common goal: enhance our understanding of the interplays between algebraic invariant theory and special connections on bundles and build a transatlantic research group ready to weigh in on the new challenges of Geom…
The Aluffi algebra is an algebraic version of a characteristic cycle of a hypersurface in intersection theory which connects with various themes of commutative algebra. In this research project, first we study the torsion-free Aluffi algebras, the Nash Rees algebra and the Jacobian ideal of projectively embedded curves, the Aluffi algebra of space curves and singular hypersurfaces, the …
In algebraic geometry, moduli spaces are parameter spaces of geometric objects. Moduli spaces ofsheaves, in particular, have been an important area of study over the past few decades, partly because of their tight connections with theoretical physics. A typical way to construct a moduli space is to begin with a criterion that decides which sheaves will be parametrized by the moduli space;…
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…
(Only some records are available in English at this moment)
The moduli space of solutions to the equations of motion of a physical theory often carries geometric structures that encode interesting features of the theory such as its symmetries. If the physical theory is defined on some manifold, then the symmetries of the theory place nontrivial constraints on the geometry of the manifold. In particular, there is a fascinating interplay between the…
Moduli problems are one of the fundamental topics of study and research of Algebraic Geometry and they arise in connection with classification problems. Roughly speaking, a moduli problem consists of a set of geometric objects A, together with an equivalence relation < on A. The problem consists of describing the set of equivalence classes A/ < and giving to A/ < a structure that reflects…
The present project aims the understanding of Bridgeland deformation theorem, whichsays that the set of stability conditions can be given the structure of a complex manifold. In order to achieve this, it will be necessary to study the Bridgeland stability as ageneralization of stability in curves.
(Only some records are available in English at this moment)
Hilbert and Quot schemes are quite important in modern Algebraic Geometry, asthey have an important role in such areas as the construction of moduli spaces anddeformation theory. When working with Hilbert schemes of points, it is quite clear thatthe difficulty of the problems increases quite fast with the dimension of the space andthe number of points, so that any kind of generalization m…
In the paper ´Stability of equivariant logarithmic tangent sheaf on toric varieties of Picard rank two´, we studied slope stability of equivariant logaritmic tangent sheaves on smooth toric varieties. One part of this project is to study stability of logarithmic tangent sheaves when they are not equivariant. We will mainly consider the case where the variety is a complex projective space.…
This project will consist of the study of derived categories and Fourier-Mukai transforms with the objective of understanding the construction of both those objects and of their most important tools. An special focus will be given to the definition of derived categories of coherent sheaves of a scheme and their algebraic properties. As an application of the studied methods, the project wi…
(Only some records are available in English at this moment)
I am planning to work on two projects on stability conditions, which are both following my Ph.D. work. The first one is to generalize the Euler stability in my thesis to other varieties, especially the ones with strong exceptional collections. Currently, the most common construction is by tilting the heart,which becomes too complicated to handle on a variety with dimensions greater than 3…
The main project is dedicated to investigating certain freeness and stability properties oflogarithmic tangent sheaves on complete intersections in projective spaces, which are defined as the kernel of a Jacobian matrix associated to a complete intersection. The main starting point of this theory is an homonymous paper, which includes the advisor and the internship supervisor as co-author…
Bruzzo and Grassi proved a "Noether-Lefschetz theorem for toric varieties", which claims, if Y is a 2k+1-dimensional Oda projective simplicial toric variety then for a very general quasi-smooth hypersurface X with big enough degree, one has that every (k,k)-cohomology class comes from the ambient space. The Noether-Lefschetz locus is the locus of quasi-smooth hypersurfaces with the same d…
(Only some records are available in English at this moment)
| 2 / 2 | Ongoing grants |
| 24 / 24 | Completed research grants |
| 5 / 5 | Ongoing scholarships in Brazil |
| 35 / 33 | Completed scholarships in Brazil |
| 11 / 11 | Completed scholarships abroad |
| 77 / 75 | All research grants and scholarships |
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