Objective
"This proposal connects three areas that are considered distant from each other: computational complexity, algebraic geometry, and numerics. In the last decade, it became clear that the fundamental questions of computational complexity (P vs NP) should be studied in algebraic settings, linking them to problems in algebraic geometry. Recent progress on this challenging and very difficult questions led to surprising progress in computational invariant theory, which we want to explore thoroughly. We expect this to lead to solutions of computational problems in invariant theory that currently are considered infeasible. The complexity of Hilbert's null cone (the set of ""singular objects'') appears of paramount importance here. These investigations will also shed new light on the foundational questions of algebraic complexity theory. As an essential new ingredient to achieve this, we will tackle the arising algebraic computational problems by means of approximate numeric computations, taking into account the concept of numerical condition.
A related goal of the proposal is to develop a theory of efficient and numerically stable algorithms in algebraic geometry that reflects the properties of structured systems of polynomial equations, possibly with singularities. While there are various heuristics, a satisfactory theory so far only exists for unstructured systems over the complex numbers (recent solution of Smale's 17th problem), which seriously limits its range of applications. In this framework, the quality of numerical algorithms is gauged by a probabilistic analysis that shows small average (or smoothed) running time. One of the main challenges here consists of a probabilistic study of random structured polynomial systems. We will also develop and analyze numerical algorithms for finding or describing the set of real solutions, e.g. in terms of their homology.
"
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: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics algebra
- natural sciences mathematics pure mathematics geometry
- natural sciences computer and information sciences artificial intelligence heuristic programming
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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.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
ERC-ADG - Advanced Grant
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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.
(opens in new window) ERC-2017-ADG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
10623 Berlin
Germany
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.