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SYZYGY SIGNED

Syzygies, moduli and topological invariants of groups

Total Cost €

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EC-Contrib. €

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Partnership

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Project "SYZYGY" data sheet

The following table provides information about the project.

Coordinator
HUMBOLDT-UNIVERSITAET ZU BERLIN 

Organization address
address: UNTER DEN LINDEN 6
city: BERLIN
postcode: 10117
website: www.hu-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˙147˙202 €
 EC max contribution 2˙147˙202 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-ADG
 Funding Scheme ERC-ADG
 Starting year 2020
 Duration (year-month-day) from 2020-03-01   to  2025-02-28

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    HUMBOLDT-UNIVERSITAET ZU BERLIN DE (BERLIN) coordinator 2˙147˙202.00

Map

 Project objective

This is a proposal aimed at harvesting interconnections between algebraic geometry and geometric group theory using syzygies. The impetus of the proposal is the recent breakthrough in which, inspired by rational homotopy theory, we introduced Koszul modules as novel homological objects establishing striking connections between algebraic geometry and geometric group theory. Deep statements in geometric group theory have startling counterparts in algebraic geometry and these connection led to a recent proof of Green's Conjecture for generic algebraic curves in arbitrary characteristic, as well as to a dramatically simpler proof in characteristic zero. Based on a dynamic view of mathematics in which ideas from one field trigger major developments in another, I propose to lead a group at HU Berlin dedicated to the following major themes, which are outlined in the proposal: (i) Find a solution to Green's Conjecture on the syzygies of an arbitrary smooth canonical curve of genus g. Find a full solution to the Prym-Green Conjecture on the syzygies of a general paracanonical algebraic curve of genus g. Formulate and prove a non-commutative Green's Conjecture for super algebraic curves. (ii) Compute the Kodaira dimension of the moduli space of curves in the transition case from unirationality to general type, when g is between 17 and 21. Construct the canonical model of the moduli space of curves and find its modular interpretation. (iii) Find algebro-geometric interpretations for Alexander invariants of the Torelli group of the mapping class group and that of the Torelli group of the free group. Understand the link between these invariants, the homotopy type and the cohomological dimension of the moduli space of curves. (iv) Get structural insight in the newly discovered topological version of Green's Conjecture involving the Alexander invariant of the group.

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

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