Log In
Sign Up
Romania
Citizenship:
Ph.D. degree award:
Mr.
Laurentiu
Leustean
Dr. Habil.
-
Error
Personal public profile link.
Expertise & keywords
Projects
Publications & Patents
Entrepreneurship
Reviewer section
Proof mining in metric anaysis, geometric group theory and ergodic theory
Call name:
Exploratory Research Projects - PCE-2011 call
PN-II-ID-PCE-2011-3-0383
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:
http://imar.ro/~leustean/grant-idei.html
Abstract:
We shall use proof mining techniques in order to obtain finitary versions with effective bounds of some important results in metric analysis, geometric group theory (Gromov's theorem on groups with polynomial growth, approximate groups) and ergodic Ramsey theory.
Proof mining is a new paradigm of research, with researchers working at different universities in Europe and USA.
The program of proof mining is concerned with the extraction of hidden finitary and combinatorial content, such as algorithms and effective bounds, from proofs that make use of highly infinitary principles.
This research direction can be related to Terence Tao's proposal of "hard analysis", based on finitary arguments, instead of the infinitary ones from "soft analysis".
Read more
Topics in nonlinear analysis and ergodic theory on uniformly convex geodesic spaces
Call name:
Postdoctoral Research Projects - PD-2012 call
PN-II-RU-PD-2012-3-0152
2013
-
2015
Role in this project:
Key expert
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/pd30152/
Abstract:
In this project we aim to extend the theory of less regular frameworks than those normally considered in nonlinear analysis and ergodic theory and apply the findings in these fields. More precisely, we first center on investigating regularity properties of geodesic spaces with a special focus on uniformly convex ones. We intend to study the relation between uniformly convex metric spaces and other relevant classes of metric spaces that are more general than spaces of nonpositive curvature. Proof mining techniques will be applied to obtain in the context of uniformly convex spaces effective bounds for different types of results in nonlinear analysis and ergodic theory. In addition, we focus on extending noncommutative ergodic theorems to more general settings.
Read more
Optimized program synthesis from proofs
Call name:
Projects for Young Research Teams - TE-2011 call
PN-II-RU-TE-2011-3-0122
2011
-
2014
Role in this project:
Key expert
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/te201130122/
Abstract:
Light functional interpretations were introduced by Hernest in his PhD thesis as optimizations of Goedel´s Dialectica interpretation and its monotone variant due to Kohlenbach by adaptation of the uniform quantifiers due to Berger (in a Modified Realizability setting) to the Dialectica context. This was continued with Trifonov by refining the detection of the uniform parts of a quantifier, which implied the addition of new semi-uniform quantifiers. The latest device for more efficient program extraction from proofs is the modal operator, which discards the request for negative computational content from its whole quantified formula. Illustrative applications were presented for all the light tools. We wish to find not only new, but also more complex applications of these light techniques. We target two large classes of applications. The first is new algorithms for various combinatorial problems for which at most certain heuristic approaches yield somewhat better results than the blunt search in the solutions space. The second is related to the Proof Mining project of Kohlenbach: in his 2008 book he outlines four ambitious research directions for the construction of new quantitative (sometimes qualitative) data out of existing recent celebrated proofs in Mathematics. We also want to compare the output of the light modal Dialectica interpretation with that of Escardo and Oliva's Pierce translation on certain classical proofs of mathematical theorems in the proof-assistat MinLog
Read more
FILE DESCRIPTION
DOCUMENT
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
[T: 0.1713, O: 134]