Abstract
The aim of this project is to introduce the student to modern algebraic geometry machinery, culminating in the proof of the classic Riemann-Roch theorem by means of beam cohomology and Serre's duality.
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Kostiantyn Iusenko
CV Lattes
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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Ucrânia
Holds a PhD in Representations of Involutive Algebras from the Institute of Mathematics (Kyiv, Ukraine) obtained in 2008. Currently, he is an associate professor, MS-5, at the University of São Paulo. He has experience in the field of Mathematics, with an emphasis on Representation Theory. Research Focus: geometric, homological, and categorical aspects of algebra representations. (Source: Lattes Curriculum)
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Research grants
- Geometry in Algebra and Algebra in Geometry VII, AO.R
- Sixth Conference on Geometric Methods in Representation Theory, AR.EXT
- Geometry in Algebra and Algebra in Geometry IV, AO.R
(Only some records are available in English at this moment)
Scholarships in Brazil
- The Riemann-Roch theorem and the Serre duality, BP.IC
- Moduli spaces of vector bundles on projective varieties, BP.IC
Abstract
This project aims to introduce the student with basic concepts about projective varieties, vector bundles on projective varieties, moduli spaces and the basic methods of representation theory (of quivers and posets) to study some moduli problems in algebraic geometry.
- Stable vector bundles over projective plane and representations of posets in the category of unitary spaces, BP.PD
Abstract
This project is aimed to study the representation theory of partially ordered sets in unitary spaces with additional linear relation. Importance of such objects is due to their applications to moduli problems such as: description of toric vector bundles over projective plane, description of rigid unitary representations of the fundamental group over punctured disc among the others. (AU)
Total / Available in English
| 5 / 5 | Completed research grants |
| 3 / 3 | Completed scholarships in Brazil |
| 8 / 8 | All research grants and scholarships |
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