Objective
A lattice is defined as the set of all integer combinations of $n$ linearly independent vectors in $\R^n$. These geometrical objects possess a rich combinatorial structure that has attracted the attention of great mathematicians over the last two centuries. Lattices have an impressive number of applications in mathematics and computer science, from number theory and Diophantine approximation to complexity theory and cryptography. Over the last two decades, the computational study of lattices has witnessed several remarkable discoveries. Most notable are the development of the LLL algorithm by Lenstra, Lenstra and Lovasz and Ajtai's discovery of lattice-based cryptographic constructions. I propose to pursue these research directions and attempt to discover new connections between lattices and computer science. A particular focus will be put on applications in cryptography, as these can lead to many advances in the field and are also of great practical importance. I believe that the extraordinary properties of lattices have the potential to revolutionize many other areas of computer science such as complexity, cryptography, machine learning theory, quantum computation, and more. My scientific goals include obtaining stronger and more practical lattice-based cryptographic constructions, resolving important questions regarding the complexity of lattice problems, finding sub-exponential time algorithms for lattice problems and exploring some novel applications of lattices to areas such as Markov chains and machine learning theory.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences computer and information sciences computer security cryptography
- natural sciences mathematics pure mathematics arithmetics
- natural sciences computer and information sciences artificial intelligence machine learning
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
ERC-2007-StG
See other projects for this call
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Host institution
75794 Paris
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.