Positivity in Lie groups and representation varieties

Project Information

PosLieRep

Grant agreement ID: 101018839

DOI

10.3030/101018839

EC signature date 22 May 2021

Start date 1 October 2021

End date 30 September 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 028 016,00

EU contribution

€ 2 028 016,00

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Non-peer reviewed articles (3)

Generalizing Lusztig’s total positivity

Author(s): Olivier Guichard, Anna Wienhard
Published in: Inventiones mathematicae, Issue 239, 2025, Page(s) 707-799, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-024-01303-y

Fiber bundles associated with Anosov representations

Author(s): Daniele Alessandrini, Sara Maloni, Nicolas Tholozan, Anna Wienhard
Published in: Forum of Mathematics, Sigma, Issue 13, 2025, Page(s) 1-46, ISSN 2050-5094
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/fms.2025.4

SL2-like properties of matrices over noncommutative rings and generalizations of Markov numbers

Author(s): Zachary Greenberg, Dani Kaufman, Anna Wienhard
Published in: Advances in Mathematics, Issue 482, 2025, Page(s) 110556, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2025.110556

Other (23)

Invariant multi-functions and Hamiltonian flows for surface group representations

Author(s): Fernando Camacho-Cadena, James Farre, Anna Wienhard
Published in: arxiv, 2024, Page(s) 66
Publisher: arxiv
DOI: 10.48550/arxiv.2410.05154

Thurston's asymmetric metrics for Anosov representations

Author(s): Carvajales, León; Dai, Xian; Pozzetti, Beatrice; Wienhard, Anna
Published in: arXiv, 2022, Page(s) 56
Publisher: arXiv
DOI: 10.48550/arxiv.2210.05292

Dominating manifolds by radial balls

Author(s): Samuel Bronstein
Published in: arXiv, 2025, Page(s) 24
Publisher: arXiv
DOI: 10.48550/arxiv.2506.15621

Fock bundles and Hitchin components

Author(s): Georgios Kydonakis, Charlie Reid, Alexander Thomas
Published in: arXiv, 2023, Page(s) 60
Publisher: arXiv
DOI: 10.48550/arxiv.2310.04377

Zariski-Closures of Linear Reflection Groups

Author(s): Jacques Audibert, Sami Douba, Gye-Seon Lee, Ludovic Marquis
Published in: arxiv, 2025, Page(s) 34
Publisher: arxiv
DOI: 10.48550/arxiv.2504.01494

Volume, entropy, and diameter in SO(p,q+1)-higher Teichmüller spaces

Author(s): Filippo Mazzoli, Gabriele Viaggi
Published in: arXiv, 2023, Page(s) 32
Publisher: arXiv
DOI: 10.48550/arxiv.2312.17137

Spectral Networks: Bridging higher-rank Teichmüller theory and BPS states

Author(s): Clarence Kineider, Georgios Kydonakis, Eugen Rogozinnikov, Valdo Tatitscheff, Alexander Thomas
Published in: arxiv, 2024, Page(s) 353
Publisher: arxiv
DOI: 10.48550/arxiv.2412.03588

Restrictions on Anosov subgroups of Sp(2n,R)

Author(s): Dey, Subhadip; Greenberg, Zachary; Riestenberg, J. Maxwell
Published in: arXiv, 2023, Page(s) 20
Publisher: arXiv
DOI: 10.48550/arxiv.2304.13564

Symplectic groups over Lie subgroups of involutive algebras

Author(s): Eugen Rogozinnikov
Published in: arXiv, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2510.11267

Structure constants for simple Lie algebras from principal sl2-triple

Author(s): Abdelmalek Abdesselam, Alexander Thomas
Published in: arXiv, 2023, Page(s) 35
Publisher: arXiv
DOI: 10.48550/arxiv.2309.08213

Noncommutative Polygonal Cluster Algebras

Author(s): Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard
Published in: arxiv, 2024, Page(s) 64
Publisher: arxiv
DOI: 10.48550/arxiv.2410.08813

Multiplicative Inequalities In Cluster Algebras Of Finite Type

Author(s): Michael Gekhtman, Zachary Greenberg, Daniel Soskin
Published in: arxiv, 2024, Page(s) 20
Publisher: arxiv
DOI: 10.48550/arxiv.2409.06642

Positivity and representations of surface groups

Author(s): Olivier Guichard, François Labourie, Anna Wienhard
Published in: 2021, Page(s) 42
Publisher: arXiv
DOI: 10.48550/arxiv.2106.14584

Topology of the space of d-pleated surfaces

Author(s): Sara Maloni, Giuseppe Martone, Filippo Mazzoli, Tengren Zhang
Published in: arXiv, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2508.04813

Symmetric spaces for groups over involutive algebras and applications to Higgs bundles

Author(s): Pengfei Huang, Georgios Kydonakis, Eugen Rogozinnikov, Anna Wienhard
Published in: arXiv, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2509.02002

Connected components of the space of triples of transverse partial flags in SO_0(p,q) and Anosov representations

Author(s): Clarence Kineider, Roméo Troubat
Published in: arxiv, 2024, Page(s) 36
Publisher: arxiv
DOI: 10.48550/arxiv.2411.08679

(BAA)-branes from higher Teichmüller theory

Author(s): Eric Y. Chen, Enya Hsiao, Mengxue Yang
Published in: arXiv, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2508.09562

Parametrizing spaces of positive representations

Author(s): Guichard, Olivier; Rogozinnikov, Eugen; Wienhard, Anna
Published in: arXiv, 2022, Page(s) 26
Publisher: Preprint
DOI: 10.48550/arxiv.2210.11605

Filtered Stokes G-local systems in nonabelian Hodge theory on curves

Author(s): Pengfei Huang, Hao Sun
Published in: arXiv, 2024, Page(s) 24
Publisher: arXiv
DOI: 10.48550/arxiv.2404.13553

Self-intersecting curves on a pair of pants and periodic orbits of Hamiltonian flows

Author(s): Fernando Camacho Cadena
Published in: arXiv, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2507.19191

Positivity, cross-ratios and the Collar Lemma

Author(s): Jonas Beyrer, Olivier Guichard (UNISTRA), François Labourie (UniCA), Beatrice Pozzetti, Anna Wienhard
Published in: arxiv, 2024, Page(s) 52
Publisher: arxiv
DOI: 10.48550/arxiv.2409.06294

Infinitesimal modular group: q-deformed sl2 and Witt algebra

Author(s): Alexander Thomas
Published in: 2023, Page(s) 16
Publisher: ArXiv
DOI: 10.48550/arxiv.2308.06158

Parahoric reduction theory of formal connections (or Higgs fields)

Author(s): Zhi Hu, Pengfei Huang, Ruiran Sun, Runhong Zong
Published in: arXiv, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2409.05073

Peer reviewed articles (5)

Maximal representations in lattices of the symplectic group

Author(s): Jacques Audibert
Published in: Geometriae Dedicata, Issue 219, 2025, Page(s) 2933–2967, ISSN 0046-5755
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10711-025-00979-7

Zariski-dense Hitchin representations in uniform lattices

Author(s): Jacques Audibert
Published in: Mathematische Annalen, Issue 392, 2025, Page(s) 2933-2967, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-025-03166-x

Restrictions on Anosov subgroups of (2,ℝ)

Author(s): Subhadip Dey, Zachary Greenberg, J. Riestenberg
Published in: Transactions of the American Mathematical Society, 2024, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9257

Cluster modular groups of affine and doubly extended cluster algebras

Author(s): Dani Kaufman, Zachary Greenberg
Published in: Mathematische Zeitschrift, Issue 310, 2025, Page(s) 50, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-025-03708-8

On partial abelianization of framed local systems

Author(s): Clarence Kineider, Eugen Rogozinnikov
Published in: Mathematische Annalen, Issue 392, 2025, Page(s) 797-836, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-025-03093-x