math.SG

Symplectic Geometry

Hamiltonian systems, symplectic flows, classical integrable systems

math.DG arXiv:2610.22288

One hyperkähler space unifies three deformation geometries

A single mapping-class-invariant structure recovers three known metrics on surface-group deformation spaces.

By Christian El Emam, Filippo Mazzoli, Nicholas Rungi and 2 more · “Extending Donaldson's HyperK\"ahler Structure via Minimal Surfaces into PSL(2,mathbb{C})”

arXiv submitted 2026-10-15 · Pith reviewed 2026-10-16 Pith rank: recent upvotes, halved daily

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math.DS arXiv:2610.16640

Zero entropy proved for real-analytic integrable geodesic flows

A 1992 conjecture of Paternain is resolved, showing real-analytic Liouville integrability prevents chaos in geodesic flows on any closed…

By Fei Liu, Xiaokai Liu, Xiang Zhang · “Analytic Liouville Integrable Geodesic Flow Has Zero Entropy”

arXiv submitted 2026-10-12 · Pith reviewed 2026-10-14 Pith rank: recent upvotes, halved daily

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math.SG arXiv:2610.22175

Viterbo's generalized conjecture falls to a magnetic flow

In disc cotangent bundles, one autonomous Hamiltonian drives Lagrangians apart at a linear rate, refuting boundedness.

By Filip Broćić, Baptiste Serraille, Ibrahim Trifa · “A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle”

arXiv submitted 2026-10-15 · Pith reviewed 2026-10-16 Pith rank: recent upvotes, halved daily

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Every invariant generalized complex torus now has a derived category

math.DG arXiv:2610.21960 reviewed 2026-10-16

A polynomial counts pillowcase triangles

math.GT arXiv:2610.21153 reviewed 2026-10-16

Wahl defect hits every nonpositive value

math.AG arXiv:2610.21093 reviewed 2026-10-16

Classified: every surface smoothing to a rational homology disk

math.AG arXiv:2610.21092 reviewed 2026-10-16

Zero net area forces four curves to inscribe a square

math.SG arXiv:2610.21076 reviewed 2026-10-16

Multiplication builds Poisson integrators that hit exact flow

math.SG arXiv:2610.20911 reviewed 2026-10-16

Distinct epsilon-positive Lagrangians have positive distance

math.SG arXiv:2610.20177 reviewed 2026-10-15

Solvmanifold cohomology reduces to eigenvalue subset sums

math.DG arXiv:2610.20153 reviewed 2026-10-15

Self-linking number predicts contact homology after (+1)-surgery

math.SG arXiv:2610.19333 reviewed 2026-10-15

Homological BFV model recovers reduced Courant algebroids

math.SG arXiv:2610.19170 reviewed 2026-10-15

All smooth members of 18 Fano fourfold families are irrational

math.AG arXiv:2610.18489 reviewed 2026-10-14

One symplectic form per manifold enforces EBK condition on all Lagrangians

math.SG arXiv:2610.17890 reviewed 2026-10-14

Discrete trajectory learning targets a modified Hamiltonian

math.NA arXiv:2610.17835 reviewed 2026-10-14

Symplectic 4-manifolds inside hyperbolic π-orbifolds

math.GT arXiv:2610.15698 reviewed 2026-10-14

One sphere inside a leaf erases every contact point

math.SG arXiv:2610.13927 reviewed 2026-10-12

Complex automorphisms approximate every Hamiltonian diffeomorphism

math.SG arXiv:2610.13718 reviewed 2026-10-12

Noncommutative open WDVV equations determine all disk invariants

math.SG arXiv:2610.13209 reviewed 2026-10-12

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Most relied on in math.SG

arXiv papers in this field that the most other arXiv papers use, build on, compare with or cite as support, read from their citing sentences.

Quantum Structures for Lagrangian Submanifolds 29 rely on it · 26 use its method · 8 build on it
Sectorial descent for wrapped Fukaya categories 28 rely on it · 18 use its method · 3 build on it
Technical details on Kuranishi structure and virtual fundamental chain 21 rely on it · 11 use its method · 2 build on it · 2 contest it
Sheaf quantization in Weinstein symplectic manifolds 19 rely on it · 16 use its method · 2 build on it
Loose Legendrian embeddings in high dimensional contact manifolds 18 rely on it · 12 use its method · 1 build on it
Symplectic cohomology and duality for the wrapped Fukaya category 18 rely on it · 10 use its method · 3 build on it
Microlocal Morse theory of wrapped Fukaya categories 18 rely on it · 8 use its method · 3 build on it
Complex cobordism, Hamiltonian loops and global Kuranishi charts 17 rely on it · 16 use its method · 5 build on it · 1 contest it