BrainMap

Mr. Liviu Ornea

Professor

Professor - UNIVERSITATEA BUCURESTI

Other affiliations

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

Researcher | Teaching staff

ResearcherID: F-1800-2010

Curriculum Vitae (08/01/2019)

Expertise & keywords

Locally conformally Kaehler geometry and related structures Call name: Exploratory Research Projects - PCE-2011 call
PN-II-ID-PCE-2011-3-0118 2012 - 2016

Role in this project:

Coordinating institution: Universitatea din Bucuresti

Project partners: Universitatea din Bucuresti (RO)

Affiliation: Universitatea din Bucuresti (RO)

Project website: http://gta.math.unibuc.ro/vuli/eng.html

Abstract:

Locally conformally Kaehler (LCK) geometry is concerned with complex manifolds of complex dimension at least two admitting a Kaehler covering with deck transformations acting by holomorphic homotheties with respect to the Kaehler metric. It is thus a part of complex differential geometry and can be treated using complex methods, Riemannian methods and algebraic geometry methods. The goal of the project is to push forward the knowledge in LCK geometry. We want to further clarify the differences between LCK and Kaehler, and to apply techniques from LCK geometry to other fields. Among the specific objectives we mention the following: we want to determine if the blow-up along subvarieties preserves the LCK class, we study (holomorphic) bundles over LCK manifolds and/or which carry LCK structures (in particular, elliptic bundles over Kaehler bases), toric LCK manifolds (aiming at a Delzant type theorem), harmonic maps and morphisms in LCK setting, indefinite LCK metrics, applications of LCK results and methods to almost contact metric geometries.

Algebraic and combinatorial tools in topology Call name: Postdoctoral Research Projects - PD-2011 call
PN-II-RU-PD-2011-3-0149 2011 - 2013

Role in this project:

Coordinating institution: Universitatea din Bucuresti

Project partners: Universitatea din Bucuresti (RO)

Affiliation:

Project website: https://dl.dropbox.com/u/109689563/CNCS_grant.html

Abstract:

Our project, “Algebraic and combinatorial tools in topology” focuses on combinatorial determination in the field of complex hyperplane arrangements, and the study of (relative) cohomology jump loci of a space in relation to (partial) formality. My aim is to pursue and extend the main directions of investigation of my thesis. One specific objective is to investigate how various aspects of the topology of the complement of an arrangement are reflected by the intersection lattice. This is a recurent research theme for the field and a general expression for major open problems of this theory, for instance combinatoriality of the Milnor fiber monodromy or of the twisted coefficients cohomology. Using, for certain classes of hyperplane arrangements, techniques introduced by Jambu-Papadima [Topology 1998] and Dimca-Papadima [Annals of Math. 2003] we relate the pattern of intersections of hyperplanes (the combinatorics) to homotopical features of the complement. The methods of homotopical algebra developed by Quillen [Annals of Math.1969] and Sullivan [Publ. IHES 1977]) provide powerful tools in topology and geometry. In this direction, as a second objective, we plan to explore new applications of some recently developed concepts: the relative characteristic and resonance varieties [Dimca-Papadima-Suciu, Duke Math. J. 2009] and partial formality properties [M., J. Pure Appl. Alg., 2010].

FILE DESCRIPTION	DOCUMENT
List of research grants as project coordinator	Download (22.5 kb) 04/04/2015
List of research grants as partner team leader	Download (23.5 kb) 04/04/2015
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 (22 kb) 25/11/2019