BrainMap

Mr. Marian Aprodu

Prof.

Professor - UNIVERSITATEA BUCURESTI

Other affiliations

Senior Researcher 1 - INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (Romania)

Researcher

Curriculum Vitae (10/10/2019)

Expertise & keywords

Syzygies, invariants and classification problems in algebraic geometry and topology Call name: P 4 - Proiecte de Cercetare Exploratorie, 2020
PN-III-P4-ID-PCE-2020-0029 2021 - 2023

Role in this project:

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation:

Project website: https://sites.google.com/view/pn-iii-p4-id-pce-2020-0029/home

Abstract:

The present project addresses some classification problems in algebraic geometry and topology. Invariants, either of numerical, geometric or algebraic nature, play a key role. At the core of proposal lies the concept of syzygy, a mathematical term invented by J. J. Sylvester to underline the existence of quadratic forms that are linearly related.

Moduli Spaces and Homological Methods in Geometry and Topology Call name: P 4 - Proiecte de Cercetare Exploratorie
PN-III-P4-ID-PCE-2016-0030 2017 - 2019

Role in this project: Project coordinator

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: https://sites.google.com/site/pniii0030/

Abstract:

The study of moduli spaces is a ubiquitous trend in modern mathematics, and a difficult subject. Their local structure, alias deformation theory, turns out to be more tractable: deformation functors are usually well–defined, even if the moduli space is not. The same phenomenon appears in deformation theory with (co)homological constraints. This subtler problem appears frequently, when the points P of the moduli space M come with a cohomology theory H. The need to understand the variation in M of H(P) leads to the local analysis of the embedded homology jump loci of M with respect to H. This setup encompasses a rich variety of important situations. The proposed research is an exploration of several problems related to homology jumps loci and geometry of moduli spaces. The research goals are linked to the nominated senior team members’ scientific interests (M. Aprodu, V. Brinzanescu, L. Maxim, S. Papadima), and rely on a close collaboration between them. The proposed research objectives will enhance our knowledge on syzygy theory and its connections with vector bundles and geometry of projective varieties, will substantially improve the understanding of the fruitful geometry–topology interactions, and will provide a fertile ground for potential applications in field theory and string theory.

Vector Bundle Techniques in the Geometry of Complex Varieties Call name: Exploratory Research Projects - PCE-2011 call
PN-II-ID-PCE-2011-3-0288 2011 - 2016

Role in this project: Project coordinator

Coordinating institution: Institutul de Matematica "Simion Stoilow" al Academiei Romane

Project partners: Institutul de Matematica "Simion Stoilow" al Academiei Romane (RO)

Affiliation: Institutul de Matematica "Simion Stoilow" al Academiei Romane (RO)

Project website: https://sites.google.com/site/pnii0288/

Abstract:

The study of vector bundles has always been central in geometry. Common examples include the tangent bundle of a differentiable or complex or projective manifold as well as flat vector bundles aka local systems, widely used in modern topology. Other examples arise naturally in modern physics, especially when the base manifold is space-time or some extension of it. In algebraic geometry, new relevant classes of varieties have been constructed using vector bundle techniques, for instance, either as jump loci or degeneracy loci, or by looking directly at various moduli spaces. Often, geometric data are encoded into vector bundles living on the manifold under study, and the desired conclusions are obtained by analyzing the cohomology or the subsheaves or the moduli of these bundles. Since vector bundles are basic ubiquitous objects in geometry, it is important to achieve a better understanding of their influence and their relations with intrinsic properties of the base manifolds. The present projects tackles some problems within this circle of ideas and reflects the current research interests of the team members. We focus on four specific research topics: Vector bundles and geometry of projective curves, Vector bundles on non-Kaehler complex manifolds, Homology with local coefficients and Vector bundles and geometry of special varieties.

Topological and analytical invariants of complex varieties Call name: Exploratory Research Projects - PCE-2012 call
PN-II-ID-PCE-2012-4-0156 2013 - 2016

Role in this project:

Coordinating institution: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE

Project partners: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Project website: http://sites.google.com/site/pnii0156

Abstract:

The main goal of this proposal is to improve the general understanding of topological and analytical properties of complex varieties, and of various moduli spaces appearing in algebraic and analytic geometry. The proposal is roughly divided into three main topics centered around ideas at the interface of geometric topology and algebraic and analytic geometry. The first topic is concerned with homotopy groups of complex varieties, a special attention being devoted to the case of hypersurface complements. We are interested in investigating fundamental groups as well as higher homotopy groups of such varieties. The second topic focuses on understanding the effect of singularities on the geometry and topology of complex hypersurfaces and of their complements. We plan to study topological and analytical invariants of hypersurfaces which measure the complexity of singularities, e.g., intrinsic invariants such as the Milnor-Hirzebruch classes, as well as invariants of hypersurface complements such as the Alexander-type invariants. The third topic deals with several questions on the local and global structure of moduli spaces and of their subvarieties, with an emphasis on the study of higher Brill-Nother loci in various moduli spaces. It is expected that results derived from this proposal will ultimately propagate to other fields where singularities and moduli spaces play an important role, including string theory and mirror symmetry.

Call name: Burse Tineri 2014
PN-II-RU-BT-2014-2-0006 2014 -

Role in this project:

Coordinating institution: UNIVERSITATEA BUCURESTI

Project partners: UNIVERSITATEA BUCURESTI (RO); INSTITUTUL DE MATEMATICA "SIMION STOILOW" AL ACADEMIEI ROMANE (RO)

Affiliation: UNIVERSITATEA BUCURESTI (RO)

Project website:

Abstract:

FILE DESCRIPTION	DOCUMENT
List of research grants as project coordinator
List of research grants as partner team leader
List of research grants as project coordinator or partner team leader
Significant R&D projects for enterprises, as project manager
R&D activities in enterprises
Peer-review activity for international programs/projects	Download (11.79 kb) 10/04/2016