Tootfinder

Brockett cost function for symplectic eigenvalues
Nguyen Thanh Son
https://arxiv.org/abs/2506.07560 https://arxiv.org/pdf/2506.07560

Brockett cost function for symplectic eigenvalues
The symplectic eigenvalues and corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theorem can be computed via minimization of a trace cost function under the symplecticity constraint. The optimal solution to this problem only offers a symplectic basis for a symplectic eigenspace corresponding to the sought symplectic eigenvalues. In this paper, we introduce a Brockett cost function and investigate the connection between its properties and the symplec…

This https://arxiv.org/abs/2212.14225 has been replaced.
link: https://scholar.google.com/scholar?q=a

Symplectic self-orthogonal quasi-cyclic codes
In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correc…

Replaced article(s) found for math.SG. https://arxiv.org/list/math.SG/new/
[1/1]:
Moduli spaces of spacefilling branes in symplectic 4-manifolds
h…

Trotter transition in BCS pairing dynamics
Aniket Patra, Emil A. Yuzbashyan, Boris L. Altshuler, Sergej Flach
https://arxiv.org/abs/2506.08657 https://

Trotter transition in BCS pairing dynamics
We Trotterize the mean-field dynamics of the integrable BCS model using symplectic integrators. The resulting chaotic dynamics is characterized by its Lyapunov spectrum and rescaled Kolmogorov-Sinai entropy. The chaos quantifiers depend on the Trotterization time step $τ$. We observe a Trotter transition at a finite step value $τ_c \approx \sqrt{N}$. While the dynamics is weakly chaotic for time steps $τ\ll τ_c$, the regime of large Trotterization steps is characterized by short temporal co…

Morita equivalence of shifted symplectic Lie n-groupoids
Milena Weiershausen
https://arxiv.org/abs/2505.24018 https://arxiv.org/pdf/2…

Morita equivalence of shifted symplectic Lie n-groupoids
Symplectic structures on higher objects like Lie groupoids have been studied for some time now, but not all of the proposed definitions are preserved under Morita equivalence of Lie groupoids, in turn giving rise to a consistent notion of symplectic stacks. Recently, this concept has been generalized to m-shifted symplectic forms on Lie n-groupoids, which are indeed preserved under Morita equivalence of Lie n-groupoids. In this paper, we give a rigorous proof for this statement.

Heute im #RTG2491Kolloquium:
What connects Symplectic Geometry so deeply with Algebraic Geometry and Low Dimensional Topology?
🧑‍🏫 Katrin Wehrheim
🏫 Department of Mathematics, UC Berkley
🗓️ Datum: 12.06.2025
🕓 Uhrzeit: 16:15 Uhr
📍 Sitzungszimmer, Mathematisches Institut, Bunsenstraße 3-5

This https://arxiv.org/abs/2308.14531 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Homotopy of blow ups after looping
The homotopy theory of the blow up construction in algebraic and symplectic geometry is investigated via two approaches. The first approach introduces and develops fibrewise surgery theory, for which the fibrewise framing is characterized by the homotopy groups of a certain gauge group. This is used to obtain a homotopy decomposition of the based loop space on a blow up that holds $p$-locally for all but finitely many primes $p$ and holds rationally. The second approach is purely homotopy theor…

A new addition to the zoo of isolated symplectic singularities
Callum Berry
https://arxiv.org/abs/2505.24524 https://arxiv.org/pdf/25…

A new addition to the zoo of isolated symplectic singularities
We give details of a new isolated symplectic singularity found in an affine chart in a crepant partial resolution of $\mathbb{C}^4/G_5$, which is 4-dimensional, isolated, and locally simply-connected. We distinguish the new singularity among all known such by the fact that the projective tangent cone at the singularity is non-reduced. We also find all 12 of its $\mathbb{Q}$-factorial terminalisations, in the process finding 24 for the quotient singularity $\mathbb{C}^4/G_5$.

Unknottedness of symplectic submanifold fillings
Zhengyi Zhou
https://arxiv.org/abs/2506.06807 https://arxiv.org/pdf/2506.06807

Unknottedness of symplectic submanifold fillings
We show that any symplectic filling of the standard contact submanifold $(\mathbb{S}^{2n-1},ξ_{\mathrm{std}})$ of $(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ in $(\mathbb{D}^{n+1},ω_{\mathrm{std}})$ is smoothly unknotted if $n\ge 2$. We also give a self-contained proof of the Siefring intersection formula between punctured holomorphic curves and holomorphic hypersurfaces used in the proof using the $L$-simple setup of Bao-Honda.

Explicit Symplectic Integrators for Massive Point Vortex Dynamics in Binary Mixture of Bose--Einstein Condensates
Tomoki Ohsawa
https://arxiv.org/abs/2506.03486

Explicit Symplectic Integrators for Massive Point Vortex Dynamics in Binary Mixture of Bose--Einstein Condensates
We construct explicit integrators for massive point vortex dynamics in binary mixture of Bose--Einstein condensates proposed by Richaud et al. The integrators are symplectic and preserve the angular momentum of the system exactly. Our main focus is the small-mass regime in which the minor component of the binary mixture comprises a very small fraction of the total mass. The solution behaviors in this regime change significantly depending on the initial momenta: they are highly oscillatory unles…

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Mason Faldet, Clayton Shonkwiler
https://arxiv.org/abs/2505.22847 https://

Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Unit-norm tight frames in finite-dimensional Hilbert spaces (FUNTFs) are fundamental in signal processing, offering optimal robustness to noise and measurement loss. In this paper we introduce the Eigenlift algorithm for sampling random FUNTFs. Our approach exploits the symplectic geometry of the FUNTF space, which we characterize as a symplectic reduction of frame space by a symmetry group. We then define a Hamiltonian torus action on this reduced space whose momentum map induces a fiber bundl…

Systolic inequalities on the sphere from symplectic embeddings
Brayan Ferreira
https://arxiv.org/abs/2506.07674 https://arxiv.org/pdf…

Systolic inequalities on the sphere from symplectic embeddings
We use properties of symplectic capacities that were recently defined by Hutchings to obtain upper bounds on the minimal action of Reeb orbits on fiberwise star-shaped hypersurfaces $Σ\subset T^*S^2$. In addition, we introduce the notion of a fiberwise $β$-balanced hypersurface $Σ\subset T^*S^2$ and establish upper bounds for the systole in terms of $β$ and geometric data, in the case of Riemannian metrics on $S^2$ satisfying this property. Finally, under the assumption of antipodal symmetr…

This https://arxiv.org/abs/2504.19466 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The partial derivative of ratios of Schur polynomials and applications to symplectic quotients
We show that a ratio of Schur polynomials $s_λ/s_ρ$ associated to partitions $λ$ and $ρ$ such $λ\subsetneqρ$ has a negative partial derivative at any point where all variables are positive. This is accomplished by establishing an injective map between sets of pairs of skew semistandard Young tableaux that preserves the product of the corresponding monomials. We use this result and the description of the first Laurent coefficient of the Hilbert series of the graded algebra of regular funct…

Analytic Uniqueness of Ball Volume Interpolation: Categorical Invariance and Universal Characterization
Andreu Ballus Santacana
https://arxiv.org/abs/2506.06885

Analytic Uniqueness of Ball Volume Interpolation: Categorical Invariance and Universal Characterization
We show that the classical volume formula for the unit $x$-ball, \[ V_x = \frac{π^{x/2}}{Γ(x/2+1)}, \] can be characterized as the \emph{unique} analytic continuation of Haar measure normalization and unit ball volumes for $\mathrm{O}(n)$, under principles of categorical invariance and normalization at integer dimensions. We generalize this result to the unitary and symplectic cases, formalize invariance using categorical language, and construct explicit categorical examples with functorial d…

This https://arxiv.org/abs/2406.06819 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures
We classify the almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0 \ltimes_A \mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal $\mathbb R^{2n-1}$, and the existence of complex or symplectic structures on $\mathfrak g_A$ imposes restrictions on the Jordan normal form of $A$. The classification essentially reduces to the case when $A$ is nilpotent, so we start by considering this case. …

This https://arxiv.org/abs/2404.09284 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Deriving a GENERIC system from a Hamiltonian system
We reconsider the fundamental problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system which includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians, energy, and entropy and the induced geometric structures such as Poisson and Onsager brackets (symplectic and dissipative brackets). We start from a general finite-dimensional Hamiltonian system that is coupled linearly to an infinite-dimensional…

This https://arxiv.org/abs/2503.01779 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Curvature, macroscopic dimensions, and symmetric products of surfaces
We present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. We show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with positive scalar curvature. For example, we prove that symmetric products of surfaces sharply distinguish between two distinct notions of macroscopic dimension introduced by Gromov and the second-named author. As a natural generalization of this circle of ide…

[2025-06-13 Fri (UTC), 2 new articles found for math.SG Symplectic Geometry]
toXiv_bot_toot

This https://arxiv.org/abs/2502.04253 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cohomology of symmetric stacks
We construct decompositions of: (1) the cohomology of smooth stacks, (2) the Borel--Moore homology of $0$-shifted symplectic stacks, and (3) the vanishing cycle cohomology of $(-1)$-shifted symplectic stacks, assuming a good moduli space exists and the tangent space has a pointwise orthogonal structure. These conditions are satisfied by many stacks of interest, including moduli stacks of semistable $G$-bundles and (twisted) $G$-Higgs bundles on curves, $G$-character stacks of oriented c…

Concave symplectic toric fillings
Aleksandra Marinkovi\'c
https://arxiv.org/abs/2506.03912 https://arxiv.org/pdf/2506.03912

Concave symplectic toric fillings
As shown by Etnyre and Honda in [EH], every contact 3-manifold admits infinitely many concave symplectic fillings that are mutually not symplectomorphic and not related by blow ups. In this note we refine this result in the toric setting by showing that every contact toric 3-manifold admits infinitely many concave symplectic toric fillings that are mutually not equivariantly symplectomorphic and not related by blow ups. The concave symplectic toric structure is constructed on certain linear and…

This https://arxiv.org/abs/2312.03657 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multisymplecticity in finite element exterior calculus
We consider the application of finite element exterior calculus (FEEC) methods to a class of canonical Hamiltonian PDE systems involving differential forms. Solutions to these systems satisfy a local multisymplectic conservation law, which generalizes the more familiar symplectic conservation law for Hamiltonian systems of ODEs, and which is connected with physically-important reciprocity phenomena, such as Lorentz reciprocity in electromagnetics. We characterize hybrid FEEC methods whose numer…

This https://arxiv.org/abs/2505.15726 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials
Consider an $n\times k$ matrix of i.i.d. Bernoulli random numbers with $p=1/2$. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe $GL_{n}\times GL_{k}$-duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of $GL_{n}\times GL_{k}$-representation and the dimension of the exterior algebra $\bigwedge\left(\mathbb{C}^…

Symplectic Branching through Crystals
B\'arbara Muniz
https://arxiv.org/abs/2505.21738 https://arxiv.org/pdf/2505.21738

Symplectic Branching through Crystals
We give an alternative proof of Naito--Sagaki's conjecture, which states that the restriction of $gl_{2n}(\mathbb{C})$-representations to $sp_{2n}(\mathbb{C})$ can be described in terms of crystals. Using the tableau model for crystals, we construct an explicit and self-contained bijection between their highest weight elements and Sundaram's branching model.

[2025-06-12 Thu (UTC), no new articles found for math.SG Symplectic Geometry]
toXiv_bot_toot

This https://arxiv.org/abs/2401.09337 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Gravity Coupled with Scalar, SU$(n)$, and Spinor Fields on Manifolds with Null-Boundary
In this paper, we present a theory for gravity coupled with scalar, SU$(n)$ and spinor fields on manifolds with null-boundary. We perform the symplectic reduction of the space of boundary fields and give the constraints of the theory in terms of local functionals of boundary vielbein and connection. For the three different couplings, the analysis of the constraint algebra shows that the set of constraints does not form a first class system.

Symplectic semi-characteristics
Hao Zhuang
https://arxiv.org/abs/2505.14496 https://arxiv.org/pdf/2505.14496

Symplectic semi-characteristics
We study the symplectic semi-characteristic of a 4n-dimensional closed symplectic manifold. First, we define the symplectic semi-characteristic using the mapping cone complex model of the primitive cohomology. Second, using a vector field with nondegenerate zero points, we prove a counting formula for the symplectic semi-characteristic. As corollaries, we obtain an Atiyah type vanishing property and the fact that the symplectic semi-characteristic is independent of the choices of symplectic for…

This https://arxiv.org/abs/2501.18584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Corks, exotic 4-manifolds and genus functions
We prove that every 4-dimensional oriented handlebody without 3- and 4-handles can be modified to admit infinitely many exotic smooth structures, and further that their genus functions are pairwise equivalent. We furthermore show that, for any 4-manifold admitting an embedding into a symplectic 4-manifold with weakly convex boundary, its genus function is algebraically realized as those of infinitely many pairwise exotic 4-manifolds. We also prove that, for any two 4-manifolds with non-degenera…

Introduction to moduli spaces and Dirac geometry
Eckhard Meinrenken
https://arxiv.org/abs/2506.04150 https://arxiv.org/pdf/2506.04150…

Introduction to moduli spaces and Dirac geometry
Let $G$ be a Lie group, with an invariant metric on its Lie algebra $\mathfrak{g}$. Given a surface $Σ$ with boundary, and a collection of base points $\mathcal{V}\subset Σ$ meeting every boundary component, the moduli space (representation variety) $\mathcal{M}_G(Σ,\mathcal{V})$ carries a distinguished `quasi-symplectic' 2-form. We shall explain the finite-dimensional construction of this 2-form and discuss its basic properties, using quasi-Hamiltonian techniques and Dirac geometry. This ar…

This https://arxiv.org/abs/2504.15207 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Parametric Gromov width of Liouville domains
The classical Gromov width measures the largest symplectic ball embeddable into a symplectic manifold; inspired by the symplectic camel problem, we generalize this to ask how large a symplectic ball can be embedded as a family over a parameter space $N$. Given a smooth map $f: N \to Ω$, where $Ω$ is a symplectic manifold, we define the \emph{parametric Gromov width} $\mathrm{Gr}(f,Ω)$ as the supremum of capacities $a>0$ for which there exists a family of balls, parametrized by $N$, of capaci…

[2025-06-11 Wed (UTC), no new articles found for math.SG Symplectic Geometry]
toXiv_bot_toot

On novel Hamiltonian description of the nonholonomic Suslov problem
A. V. Tsiganov
https://arxiv.org/abs/2505.19594 https://arxiv.org…

On novel Hamiltonian description of the nonholonomic Suslov problem
We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the five dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in…

On singular Lagrangian fibrations and applications to symplectic embeddings I
Santiago Achig-Andrango, Renato Vianna, Alejandro Vicente
https://arxiv.org/abs/2506.01556

On singular Lagrangian fibrations and applications to symplectic embeddings I
In this paper, we construct singular Lagrangian fibrations on some examples of disk cotangent bundles in dimensions 4 and 6. As an application, we show how this construction can be used to obtain toric domains in some cases. In particular, we recover results from Ferreira, Ramos, and Vicente on the Gromov width of the disk cotangent bundle of spheres of revolution, as well as results from Ramos on the Lagrangian bidisk. We also briefly discuss how this technique can be used to study symplectic …

This https://arxiv.org/abs/2312.09214 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Shifted coisotropic structures for differentiable stacks
We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (i.e. quasi-symplectic groupoids) using twisted Dirac structures and show that it satisfies properties analogous to the corresponding derived-algebraic notion in shifted Poisson geometry. In particular, intersections of 1-coisotropics are 0-shifted Poisson. We also show that 1-shifted coisotropic structures transfer through Morita equivalences, giving a well-defined notion for differentiable stacks. Most results are for…

[2025-06-10 Tue (UTC), 4 new articles found for math.SG Symplectic Geometry]
toXiv_bot_toot

[2025-06-09 Mon (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot #toXiv_bot_new_article_summary_toot

[2025-06-06 Fri (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-06-05 Thu (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-06-04 Wed (UTC), no new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

This https://arxiv.org/abs/2504.19332 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Reeb orbits frequently intersecting a symplectic surface
Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and we also make a technical assumption that the Reeb vector field has a particular ``nice'' form near the boundary of the surface. We then show that there exist Reeb orbits which intersect the interior of the surface, with a lower bound on the frequency of thes…

This https://arxiv.org/abs/1807.03420 has been replaced.
link: https://scholar.google.com/scholar?q=a

A JSJ-type decomposition theorem for symplectic fillings
We establish a JSJ-type decomposition theorem for splitting exact symplectic fillings of contact 3-manifolds along \emph{mixed tori} -- these are convex tori satisfying a particular geometric condition. As an application, we show that if $(M,ξ)$ is obtained from $(S^3,ξ_{\mathrm{std}})$ via Legendrian surgery along a knot which has been stabilized both positively and negatively, then $(M,ξ)$ has a unique exact filling.

[2025-06-03 Tue (UTC), 5 new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-06-02 Mon (UTC), no new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-30 Fri (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-29 Thu (UTC), no new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-28 Wed (UTC), no new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-26 Mon (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-23 Fri (UTC), 1 new article found for math.SG Symplectic Geometry]
#toXiv_bot_toot

[2025-05-22 Thu (UTC), no new articles found for math.SG Symplectic Geometry]
#toXiv_bot_toot

This https://arxiv.org/abs/2406.10866 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

K-contact manifolds with minimal closed Reeb orbits
We use the Boothby-Wang fibration to construct certain simply connected K-contact manifolds and we give sufficient and necessary conditions on when such K-contact manifolds are homeomorphic to the odd dimensional spheres. If the symplectic base manifold of the fibration admits a Hamiltonian torus action, we show that on the total space of the fibration, other than the regular K-contact structures which have infinitely many closed Reeb orbits, there are K-contact structures whose closed Reeb orb…

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…