Refined invariants in combinatorics, low-dimensional topology and geometry of moduli spaces

Project Information

REFINV

Grant agreement ID: 101001159

DOI

10.3030/101001159

Project closed

EC signature date 26 February 2021

Start date 1 June 2021

End date 31 May 2026

Funded under

EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 996 023,00

EU contribution

€ 1 996 023,00

1 996 023,00

Coordinated by

UNIVERSITAT WIEN
Austria

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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

Tautological classes and symmetry in Khovanov–Rozansky homology

Author(s): Eugene Gorsky, Matthew Hogancamp, Anton Mellit
Published in: Duke Mathematical Journal, Issue 173, 2024, ISSN 0012-7094
Publisher: Duke University Press
DOI: 10.1215/00127094-2023-0063

Extriangulated ideal quotients, with applications to cluster theory and gentle algebras

Author(s): Xin Fang, Mikhail Gorsky, Yann Palu, Pierre-Guy Plamondon, Matthew Pressland
Published in: Journal of Pure and Applied Algebra, Issue 230, 2026, Page(s) 108370, ISSN 0022-4049
Publisher: Elsevier BV
DOI: 10.1016/j.jpaa.2026.108370

Modulo <i>ℓ</i> distinction problems

Author(s): Peiyi Cui, Thomas Lanard, Hengfei Lu
Published in: Compositio Mathematica, Issue 160, 2026, Page(s) 2285-2321, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x24007346

A functorial approach to rank functions on triangulated categories

Author(s): Teresa Conde, Mikhail Gorsky, Frederik Marks, Alexandra Zvonareva
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), 2024, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2024-0009

A combinatorial skewing formula for the Rise Delta Theorem

Author(s): Maria Gillespie, Eugene Gorsky, Sean Griffin
Published in: Combinatorial Theory, Issue 5, 2025, ISSN 2766-1334
Publisher: California Digital Library (CDL)
DOI: 10.5070/c65365552

Cluster deep loci and mirror symmetry

Author(s): Marco Castronovo, Mikhail Gorsky, José Simental, David Speyer
Published in: Communications of the American Mathematical Society, Issue 6, 2026, Page(s) 1021-1086, ISSN 2692-3688
Publisher: American Mathematical Society (AMS)
DOI: 10.1090/cams/76

Cluster structures on braid varieties

Author(s): Roger Casals, Eugene Gorsky, Mikhail Gorsky, Ian Le, Linhui Shen, José Simental
Published in: Journal of the American Mathematical Society, Issue 38, 2025, Page(s) 369-479, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/1048

Wreath Macdonald operators

Author(s): Daniel Orr, Mark Shimozono, Joshua Wen
Published in: Forum of Mathematics, Sigma, Issue 13, 2025, ISSN 2050-5094
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/fms.2025.10061

Unramified Gromov-Witten and Gopakumar-Vafa invariants

Author(s): Denis Nesterov
Published in: Journal of the American Mathematical Society, 2026, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/1088

"Coherent sheaves on surfaces, COHAs and deformed upper W Subscript 1 plus normal infinity <mml:math xmlns:xlink=""http://www.w3.org/1999/xlink"" xmlns:mnf=""http://cambridge.org/core/manifest"" xmlns:cup=""http://contentservices.cambridge.org"" xmlns:mml=""http://www.w3.org/1998/Math/MathML"" xmlns:m=""http://cambridge.org/core/metadata"" xmlns:core=""http://cambridge.org/core"" xmlns:c=""h"

Author(s): Anton Mellit, Alexandre Minets, Olivier Schiffmann, Eric Vasserot
Published in: Moduli, Issue 3, 2026, ISSN 2949-7647
Publisher: Cambridge University Press (CUP)
DOI: 10.1017/s2949764726100277

A combinatorial formula for the nabla operator

Author(s): Erik Carlsson, Anton Mellit
Published in: Compositio Mathematica, Issue 161, 2026, Page(s) 800-830, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x24007760

A geometric interpretation for the Delta Conjecture

Author(s): Maria Gillespie, Eugene Gorsky, Sean T. Griffin
Published in: Advances in Mathematics, Issue 500, 2026, Page(s) 111087, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2026.111087

On quasimap invariants of moduli spaces of Higgs bundles

Author(s): Denis Nesterov
Published in: Moduli, Issue 1, 2026, ISSN 2949-7647
Publisher: Cambridge University Press (CUP)
DOI: 10.1112/mod.2024.5

On the lattices of exact and weakly exact structures

Author(s): Rose-Line Baillargeon; Thomas Brüstle; Mikhail Gorsky; Souheila Hassoun
Published in: Journal of Algebra, Issue 612, 2022, Page(s) 77-109, ISSN 0021-8693
Publisher: Academic Press
DOI: 10.1016/j.jalgebra.2022.07.043

Toric stratifications of character varieties

Author(s): Anton Mellit
Published in: Publications mathématiques de l'IHÉS, Issue 142, 2026, Page(s) 153-240, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-025-00158-0

Clusters and Weaves

Author(s): Mikhail Gorsky, José Simental
Published in: Notices of the American Mathematical Society, Issue 71, 2024, Page(s) 1, ISSN 0002-9920
Publisher: Mathematical Association of America
DOI: 10.1090/noti3000

Positroid links and braid varieties

Author(s): Roger Casals, Eugene Gorsky, Mikhail Gorsky, José Simental
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), 2026, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2026-0007

Type A DAHA and doubly periodic tableaux

Author(s): Chiara Novarini; Léa Bittmann; Alex Chandler; Anton Mellit
Published in: Advances in Mathematics, Issue 416, 2023, Page(s) 108919, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2023.108919

Irreducible components of two-column $\Delta$-Springer fibers

Author(s): Connor, Joshua P.; Griffin, Sean T.; Purohit, Kavish A.
Published in: ArXiv.org, Issue 1, 2024, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2411.17222

Hereditary extriangulated categories: Silting objects, mutation, negative extensions

Author(s): Gorsky, Mikhail; Nakaoka, Hiroyuki; Palu, Yann
Published in: ArXiv.org, 2023, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2303.07134

Comparing cluster algebras on braid varieties

Author(s): Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, José Simental
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2508.03816

On Macdonald expansions of q-chromatic symmetric functions and the Stanley-Stembridge Conjecture

Author(s): Sean T. Griffin, Anton Mellit, Marino Romero, Kevin Weigl, Joshua Jeishing Wen
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2504.06936

Tautological classes for (n,n+1) torus knots

Author(s): Eugene Gorsky, Anton Mellit
Published in: Arxiv.org, 2026, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2601.16877

Ext operators for wreath Macdonald polynomials

Author(s): Seamus Albion Ferlinc, Joshua Jeishing Wen
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2508.10772

Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences

Author(s): Mikhail Gorsky, Nicholas J. Williams
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2506.08858

Hilbert schemes of points and Fulton-MacPherson compactifications

Author(s): Nesterov, Denis
Published in: Arxiv.org, Issue 1, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2501.08269

$P=W$ via $H_2$

Author(s): Hausel, Tamas; Mellit, Anton; Minets, Alexandre; Schiffmann, Olivier
Published in: ArXiv.org, 2022, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2209.05429

Spectral geometry of the curl operator on smoothly bounded domains

Author(s): Josef Greilhuber, Willi Kepplinger
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2502.13067

Degenerations in tropical compactifications and tropical intersection theory of $\bar M_{0,n}$

Author(s): Sean T. Griffin, Jake Levinson, Rohini Ramadas, Rob Silversmith
Published in: Arxiv.org, 2026, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2604.15511

Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials

Author(s): Gorsky, Mikhail; Haiden, Fabian
Published in: ArXiv.org, 2024, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2409.10154

Tesler identities for wreath Macdonald polynomials

Author(s): Marino Romero, Joshua Jeishing Wen
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2505.01732

A structural view of maximal green sequences

Author(s): Gorsky, Mikhail; Williams, Nicholas J.
Published in: ArXiv.org, 2023, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2301.08681

Refined Verlinde and Segre formula for Hilbert schemes

Author(s): Göttsche, Lothar; Mellit, Anton
Published in: ArXiv.org, 2022, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2210.01059

GKM spaces, and the signed positivity of the nabla operator

Author(s): Carlsson, Erik; Mellit, Anton
Published in: ArXiv.org, 2021, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2110.07591

Symmetric and non-symmetric F-conjectures are equivalent

Author(s): Maksym Fedorchuk, Anton Mellit
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2507.12434

Five-Term Relations for wreath Macdonald polynomials and tableau formulas for Pieri coefficients

Author(s): Marino Romero, Joshua Jeishing Wen
Published in: Arxiv.org, 2025, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2505.15606

Harish-Chandra isomorphism for cyclotomic double affine Hecke algebras

Author(s): Wen, Joshua Jeishing
Published in: ArXiv.org, 2024, ISSN 2331-8422
Publisher: Cornell University
DOI: 10.48550/arxiv.2407.07679

DAHA and Dyck path algebras

Author(s): Chiara Novarini
Published in: 2024
Publisher: University of Vienna
DOI: 10.25365/thesis.76766

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