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Deformation quantisation of exact shifted symplectic structures, with an application to vanishing cycles
J. P. Pridham
https://arxiv.org/abs/2511.07602 https://arxiv.org/pdf/2511.07602 https://arxiv.org/html/2511.07602
arXiv:2511.07602v1 Announce Type: new
Abstract: We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal derivation, a concept generalising constructions by De Wilde and Lecomte. Our formulation is sufficiently general to encompass derived algebraic, analytic and $\mathcal{C}^{\infty}$ stacks, as well as Lagrangians and non-commutative generalisations. We also show that non-degenerate shifted Poisson structures with formal derivation carry unique self-dual deformation quantisations in any setting where the latter can be formulated.
One application is that for (not necessarily exact) $0$-shifted symplectic structures in analytic and $\mathcal{C}^{\infty}$ settings, it follows that the author's earlier parametrisations of quantisations are in fact independent of any choice of associator, and generalise Fedosov's parametrisation of quantisations for classical manifolds.
Our main application is to complex $(-1)$-shifted symplectic structures, showing that our unique quantisation of the canonical exact structure, a sheaf of twisted $BD_0$-algebras with derivation, gives rise to BBDJS's perverse sheaf of vanishing cycles, equipped with its monodromy operator.
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[2025-11-14 Fri (UTC), 1 new article found for math.SG Symplectic Geometry]
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[2025-11-13 Thu (UTC), 2 new articles found for math.SG Symplectic Geometry]
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[2025-11-12 Wed (UTC), 1 new article found for math.SG Symplectic Geometry]
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[2025-11-11 Tue (UTC), 4 new articles found for math.SG Symplectic Geometry]
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Hamiltonian flow between standard module Lagrangians
Yujin Tong
https://arxiv.org/abs/2511.06431 https://arxiv.org/pdf/2511.06431 https://arxiv.org/html/2511.06431
arXiv:2511.06431v1 Announce Type: new
Abstract: In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_\theta$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting.
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Closed-string mirror symmetry for dimer models
Dahye Cho, Hansol Hong, Hyeongjun Jin, Sangwook Lee
https://arxiv.org/abs/2511.06699 https://arxiv.org/pdf/2511.06699 https://arxiv.org/html/2511.06699
arXiv:2511.06699v1 Announce Type: new
Abstract: For all punctured Riemann surfaces arising as mirror curves of toric Calabi--Yau threefolds, we show that their symplectic cohomology is isomorphic to the compactly supported Hochschild cohomology of the noncommutative Landau--Ginzburg model defined on the NCCR of the associated toric Gorenstein singularities. This mirror correspondence is established by analyzing the closed-open map with boundaries on certain combinatorially defined immersed Lagrangians in the Riemann surface, yielding a ring isomorphism. We give a detailed examination of the properties of this isomorphism, emphasizing its relationship to the singularity structure.
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Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new
[1/1]:
- Reduction of Cosymplectic groupoids by cosymplectic moment maps
Daniel L\'opez Garcia, Nicolas Martinez Alba
https://arxiv.org/abs/2403.03178 https://mastoxiv.page/@arXiv_mathSG_bot/112047445404247851
- Algebraic Lagrangian cobordisms, flux and the Lagrangian Ceresa cycle
Alexia Corradini
https://arxiv.org/abs/2501.12850 https://mastoxiv.page/@arXiv_mathSG_bot/113876409190220093
- Systolic $S^1$-index and characterization of non-smooth Zoll convex bodies
Stefan Matijevi\'c
https://arxiv.org/abs/2501.13856 https://mastoxiv.page/@arXiv_mathSG_bot/113882071591631203
- Infinite-dimensional Lagrange-Dirac systems with boundary energy flow I: Foundations
Fran\c{c}ois Gay-Balmaz, \'Alvaro Rodr\'iguez Abella, Hiroaki Yoshimura
https://arxiv.org/abs/2501.17551 https://mastoxiv.page/@arXiv_mathSG_bot/113916045279374601
- The Simplicity of the Group of Weakly Hamiltonian Diffeomorphisms on Cosymplectic Manifolds
S. Tchuiaga, P. Bikorimana
https://arxiv.org/abs/2503.10224 https://mastoxiv.page/@arXiv_mathSG_bot/114159599811622365
- Regular semisimple Hessenberg varieties with cohomology rings generated in degree two
Mikiya Masuda, Takashi Sato
https://arxiv.org/abs/2301.03762 https://mastoxiv.page/@arXiv_mathAG_bot/109669428824274443
- Billiards and Hofer's Geometry
Mark Berezovik, Konstantin Kliakhandler, Yaron Ostrover, Leonid Polterovich
https://arxiv.org/abs/2507.04767 https://mastoxiv.page/@arXiv_mathDS_bot/114817105311885626
- Geometric, topological and dynamical properties of conformally symplectic systems, normally hyper...
Marian Gidea, Rafael de la Llave, Tere M-Seara
https://arxiv.org/abs/2508.14794 https://mastoxiv.page/@arXiv_mathDS_bot/115065890424433224
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