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MSMA SIGNED

Moduli Spaces, Manifolds and Arithmetic

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

MSMA project word cloud

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

rings students spectacular points certain analoguous point parametrize objects questions akshay begin fiber bundles vary concerning anongoing space dimension theorem linear starting simplicial differential group analogues smooth williams geometric geometry representations manifolds ph origins kickstarted proven last venkatesh essentially surface homotopy speculative joint suitable groups deformations theoretic deformation universal algebraic smaller representation theory successes wiles postdocs dimensional contains motivated nature families galois madsen firmly topology parametrizes randal myself 15 varieties moduli weiss spaces had promises ofderived multiple

Project "MSMA" data sheet

The following table provides information about the project.

Coordinator	KOBENHAVNS UNIVERSITET Organization address address: NORREGADE 10 city: KOBENHAVN postcode: 1165 website: www.ku.dk 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	Denmark [DK]
Total cost	1˙991˙061 €
EC max contribution	1˙991˙061 € (100%)
Programme	1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
Code Call	ERC-2015-CoG
Funding Scheme	ERC-COG
Starting year	2016
Duration (year-month-day)	from 2016-06-01 to 2021-11-30

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	KOBENHAVNS UNIVERSITET KOBENHAVNS UNIVERSITET Organization address address: NORREGADE 10 city: KOBENHAVN postcode: 1165 website: www.ku.dk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	DK (KOBENHAVN)	coordinator	1˙991˙061.00

Map

Project objective

This proposal concerns the application of homotopy theoretic methods to multiple questions of geometric nature, and in particular the study of moduli spaces. Firmly based in topology, the research proposed here is strongly motivated by applications and potential applications to differential geometry, algebraic geometry and especially number theory. Any “moduli space” parametrizes how certain objects may vary in families. The moduli spaces of manifolds parametrize how smooth manifolds may vary in families (smooth fiber bundles), and the representation varieties studied in the second major component parametrize how linear representations of a group may vary in algebraic families.

The homotopy theoretic study of moduli spaces of manifolds has seen spectacular successes in the last 15 years, kickstarted by a theorem of Madsen and Weiss concerning the topology of moduli spaces of 2-dimensional manifolds. Very recently, anongoing collaboration between O. Randal-Williams and myself promises to establish analoguous results for manifolds of higher dimension. If funded, the research proposed here will bring this research program to a point where all major results about surface moduli spaces have proven analogues for manifolds of higher dimension. The second major component of this proposal has strong number-theoretic origins, but is essentially homotopy theoretic. It concerns the study of universal deformations of representations of (Galois) groups. If funded, the research in this component of the proposal, joint with Akshay Venkatesh, will develop derived (simplicial) deformation rings. Classical deformation rings have had spectacular applications in number theory (starting with Wiles’ work) and we also propose to begin the study of applications ofderived deformation rings.

Finally, the proposal contains smaller or more speculative projects, and points out many questions which might be suitable for the Ph.D.-students and postdocs also applied for in this proposal.

Publications

List of publications.
year	authors and title	journal	last update
2019	Manuel Krannich On characteristic classes of exotic manifold bundles published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-019-01847-y	Mathematische Annalen	2019-08-29
2020	Gijs Heuts Goodwillie approximations to higher categories published pages: accepted for pub, ISSN: 0065-9266, DOI:	Memoirs of the AMS	2019-08-29
2019	Alexander Kupers Some finiteness results for groups of automorphisms of manifolds published pages: to appear, ISSN: 1465-3060, DOI:	Geometry and Topology	2019-08-29
2020	SÃ¸ren Galatius, Alexander Kupers, Oscar Randal-Williams Cellular E_k algebras published pages: , ISSN: , DOI:	preprint	2019-08-29
2020	Alexander Kupers, Oscar Randal-Williams On the cohomology of Torelli groups published pages: , ISSN: , DOI:	preprint	2019-08-29
2019	SÃ¸ren Galatius, Alexander Kupers, Oscar Randal-Williams E 2 $E_{2}$ -cells and mapping class groups published pages: , ISSN: 0073-8301, DOI: 10.1007/s10240-019-00107-8	Publications mathÃ©matiques de l\'IHÃ‰S	2019-08-29

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