BrainMap

Mr. Cezar Oniciuc

Professor

Professor - UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Researcher

Curriculum Vitae (20/04/2020)

Expertise & keywords

CONSTANT MEAN CURVATURE AND BIHARMONIC SUBMANIFOLDS Call name: Projects for Young Research Teams - RUTE -2014 call
PN-II-RU-TE-2014-4-0004 2015 - 2017

Role in this project: Partner team leader

Coordinating institution: UNIVERSITATEA TEHNICĂ "GHEORGHE ASACHI" IAŞI

Project partners: UNIVERSITATEA TEHNICĂ "GHEORGHE ASACHI" IAŞI (RO)

Affiliation: UNIVERSITATEA TEHNICĂ "GHEORGHE ASACHI" IAŞI (RO)

Project website: http://math.etc.tuiasi.ro/dfetcu/

Abstract:

Submanifolds with constant mean curvature (CMC submanifolds) and, more generally, submanifolds with mean curvature vector field parallel in the normal bundle (PMC submanifolds) are two of the most studied objects in modern Differential Geometry. A more recent subject is represented by biharmonic immersions (biharmonic submanifolds), a particular case of biharmonic maps between Riemannian manifolds. The biharmonic maps were suggested by J. Eells and J. H. Sampson as a natural generalization of harmonic maps and, therefore, biharmonic submanifolds generalize the classical minimal submanifolds. The aim of our project is to study CMC, PMC, and biharmonic submanifolds in various geometric contexts. New examples, as well as characterization and classification results, will be obtained. Classical instruments often involved in this kind of studies, like, for example, holomorphic differentials or Simons type equations, will be used and also new methods will be developed in order to understand and describe the geometry of such submanifolds.

Combinatorial and geometric methods for studying arithmetic invariants Call name: Exploratory Research Projects - PCE-2012 call
PN-II-ID-PCE-2012-4-0640 2013 - 2016

Role in this project: Partner team leader

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI (RO)

Affiliation: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI (RO)

Project website: http://www.math.uaic.ro/~litcanu/proiect_PCE.html

Abstract:

Arithmetic geometry provides an appropriate, sophisticate and stimulating context for formulating most of the classical and modern problems in number theory. The central objective of this proposal is obtaining new results in arithmetic geometry and, more specifically, in Arakelov theory, which concern arithmetic numerical invariants and characteristic classes. A special attention will be given to explicit methods and techniques. The specific objectives of the proposal belong to three major research tasks:

1. Heights in arithmetic geometry and relations with other arithmetic invariants. Height functions will be constructed by means of more explicit and combinatoric methods, as an interplay between Belyi’s theorem and Arakelov theory.

2. Arithmetic intersection theory and height functions on algebraic stacks. For studying and computing height functions on moduli spaces one needs to extend fundamental results in Arakelov theory to algebraic stacks.

3. Arithmetic Grothendieck-Riemann-Roch formulae for general projective morphisms and applications in the study of height functions.

One of the priorities of the project is the development of the interaction of the members of the team with other researchers at European and international level.

Biharmonic maps and submanifolds in certain geometric contexts Call name: Projects for Young Research Teams - TE-2011 call
PN-II-RU-TE-2011-3-0108 2011 - 2014

Role in this project: Project coordinator

Coordinating institution: Universitatea Alexandru Ioan Cuza din Iasi

Project partners: Universitatea Alexandru Ioan Cuza din Iasi (RO)

Affiliation: Universitatea Alexandru Ioan Cuza din Iasi (RO)

Project website: http://www.math.uaic.ro/~oniciucc/TE-2011-3-0108_web/TE.html

Abstract:

A harmonic map between Riemannian manifolds is a critical point for the energy functional; the Euler-Lagrange equation associated to this functional is obtained by vanishing the tension field. The biharmonic maps arise in the work of J. Eells and J.H. Sampson as a natural generalization of harmonic maps. Accordingly, a smooth map is biharmonic if it is a critical point of the bienergy functional. In the case of submanifolds, the biharmonicity leads to biharmonic submanifolds, which represent an interesting generalization of the classical minimal submanifolds. The aim of the present project is to study the biharmonicity in various geometric contexts. This can be integrated in a wider research direction, in which new examples of biharmonic maps and new classification results for biharmonic submanifolds are anticipated to be obtained. A complementary research direction of the present project consists in the study, using cohomological methods, of some topological and algebraic properties of manifolds and submanifolds, in contexts that may lead to such properties for biharmonic submanifolds.

Cohomological methods in algebraic geometry and complex geometry Call name:
2009 - 2011

Role in this project: Partner team leader

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Affiliation: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Project website:

Abstract:

F-structures on differentiable manifolds and biharmonic properties Call name:
Grant ET, CEEX, no. 5871 2006 - 2007

Role in this project: Project coordinator

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Affiliation: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Project website:

Abstract:

Palais-Smale Condition and reduction techniques for biharmonic maps Call name:
Grant At, CNCSIS, no. 60 GR 2006 - 2007

Role in this project: Project coordinator

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Affiliation: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI ()

Project website:

Abstract:

Biharmonic maps, stability and conformal changes Call name:
Grant At, CNCSIS, no. 33373 -

Role in this project: Project coordinator

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners:

Affiliation:

Project website:

Abstract:

Biharmonic maps between Riemannian manifolds Call name:
Grant T, ANSTI, no. 6186 GR -

Role in this project: Project coordinator

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners:

Affiliation:

Project website:

Abstract:

Harmonic sections in the unit tangent bundle Call name:
Grant T, ANSTI, no. 5146 GR -

Role in this project: Project coordinator

Coordinating institution: UNIVERSITATEA "ALEXANDRU IOAN CUZA" IASI

Project partners:

Affiliation:

Project website:

Abstract:

FILE DESCRIPTION	DOCUMENT
List of research grants as project coordinator	Download (249.94 kb) 30/03/2017
List of research grants as partner team leader	Download (68.27 kb) 30/03/2017
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