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COCAN SIGNED

Complexity and Condition in Algebra and Numerics

Total Cost €

EC-Contrib. €

Partnership

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COCAN project word cloud

Explore the words cloud of the COCAN project. It provides you a very rough idea of what is the project "COCAN" about.

equations distant foundational stable numerically seriously computational approximate gauged solutions analyze ingredient describing infeasible null reflects complexity running small consists connects framework computations np hilbert questions light quality difficult 17th investigations algebraic homology random last fundamental numerics smale limits singular cone time arising objects clear possibly satisfactory numeric invariant became structured appears vs decade paramount geometry probabilistic explore linking surprising progress singularities algorithms numerical led settings solution tackle shed polynomial theory shows exists heuristics efficient unstructured thoroughly smoothed

Project "COCAN" data sheet

The following table provides information about the project.

Coordinator	TECHNISCHE UNIVERSITAT BERLIN Organization address address: STRASSE DES 17 JUNI 135 city: BERLIN postcode: 10623 website: www.tu-berlin.de contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	Germany [DE]
Total cost	2˙297˙163 €
EC max contribution	2˙297˙163 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2017-ADG
Funding Scheme	ERC-ADG
Starting year	2019
Duration (year-month-day)	from 2019-01-01 to 2023-12-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	TECHNISCHE UNIVERSITAT BERLIN TECHNISCHE UNIVERSITAT BERLIN Organization address address: STRASSE DES 17 JUNI 135 city: BERLIN postcode: 10623 website: www.tu-berlin.de contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	DE (BERLIN)	coordinator	2˙297˙163.00

Map

Project 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. '

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The information about "COCAN" are provided by the European Opendata Portal: CORDIS opendata.