Projects Inventory

Symplectic Geometry Research Project Examples

  1. Coupling Dynamic characteristics of Simplified Model for Tethered Satellite System
  2. On exceptional Lie geometries
  3. On the Carathéodory Form in Higher-Order Variational Field Theory
  4. A characterization of the alpha-connections on the statistical manifold of normal distributions
  5. Poisson principal bundles
  6. A geometric characterization of the finitary special linear and unitary Lie algebras


  1. On the Scalar Curvature of 4-Manifolds
  2. The quantum canonical ensemble in phase space
  3. Estimating Reeb chords using microlocal sheaf theory
  4. Differential invariants for flows of fluids and gases
  5. Branched covering simply-connected 4-manifolds
  6. A discrete differential geometry-based approach to buckling and vibration analyses of inhomogeneous Reddy plates
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  8. Integrable Deformations and Dynamical Properties of Systems with Constant Population
  9. Quasipositive links and Stein surfaces
  10. Hamiltonian knottedness and lifting paths from the shape invariant
  11. On -points of -analogs of the Fano plane


  1. The structure of quaternionic Kähler quotients
  2. Birkhoff and symplectic billiards; an overview
  3. Classification of Left Invariant Riemannian metrics on Complex hyperbolic space
  4. A Boothby–Wang theorem for Besse contact manifolds
  5. Extended corner symmetry, charge bracket and Einstein’s equations
  6. Symmetry Reduction of States I
  7. The QR decomposition for radial neural networks
  8. Extended Hamilton–Jacobi Theory, Symmetries and Integrability by Quadratures
  9. Infinite Lifting of an Action of Symplectomorphism Group on the set of some Bi-Lagrangian Structures
  10. Symplectic Runge–Kutta discretization of a regularized forward–backward sweep iteration for optimal control problems


  1. Symmetry Fundamentalism: A Case Study from Classical Physics
  2. Gluing Non-commutative Twistor Spaces
  3. Steinberg slices and group-valued moment maps
  4. Lagrangian Cobordisms in Liouville manifolds
  5. One-dimensional Center Symmetric Local Binary Pattern Based Epilepsy Detection Method
  6. Whiskered Tori for Presymplectic Dynamical Systems
  7. Stochastic geometric mechanics with diffeomorphisms
  8. Symplectic approach for plane elasticity problems of two-dimensional octagonal quasicrystals
  9. Symplectic wave-based method for free and steady state forced vibration analysis of thin orthotropic circular cylindrical shells with arbitrary boundary conditions
  10. Elliptic isometries of the manifold of positive definite real matrices with the trace metric


  1. Geometric numerical integration of Liénard systems via a contact Hamiltonian approach
  2. Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic te…
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  4. A K-contact simply connected -manifold with no semi-regular Sasakian structure
  5. Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction
  6. Shadowing Homoclinic Chains to a Symplectic Critical Manifold
  7. Currents, charges and algebras in exceptional generalised geometry
  8. An Geometrization on the quantum dynamics of two-component Bose-Einstein Condensate
  9. Torelli theorem for the moduli space of symplectic parabolic Higgs bundles
  10. Algebra and geometry of link homology
  11. On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms


  1. The John Conway Hour, NTBA
  2. Low Dimensional Supersymmetric Gauge Theories and Mathematical Applications
  3. A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting
  4. Moduli Spaces of Higgs Bundles–Old and New
  5. Scalar curvature and the moment map in generalized Kahler geometry
  6. Microscopic shell-model counterpart of the Bohr–Mottelson model
  7. Dynamical Quantization of Contact Structures
  8. Geometric Numerical Integration (hybrid meeting)
  9. Applications of metaplectic cohomology and global-local contact holonomy
  10. Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold


  1. Equivariant and supersymmetric localization in QFT
  2. The tools of mechanics by E. Cartan and classical field theory
  3. Revisiting the averaged problem in the case of mean-motion resonances of the restricted three-body problem. Global rigorous treatment and application to the co …
  4. When scale is surplus
  5. Tropical Lagrangians in toric del-Pezzo surfaces
  6. Dressing operators in equivariant Gromov-Witten theory of
  7. BV and BFV for the H-twisted Poisson sigma model
  9. The symplectic s-cobordism conjecture: a summary
  10. Lectures on Mathematical Methods in Physics


  1. Nonassociative analogs of Lie groupoids
  2. Non-commutative integrability, exact solvability and the Hamilton–Jacobi theory
  3. Generalising G 2 geometry: involutivity, moment maps and moduli
  4. Tau function and moduli of meromorphic quadratic differentials
  5. Sheaf theoretic compactifications of the space of rational quartic plane curves
  6. Superconformal geometries and local twistors
  7. Equivariant deformation quantization and coadjoint orbit method
  8. Magnetized Kepler manifolds and their quantization
  9. Riemann soliton within the framework of contact geometry
  10. Solvable Lie algebras and solvmanifolds


  1. Conway Subgroup Symmetric Compactifications Redux
  2. Relations for Grothendieck groups of -cluster tilting subcategories
  3. Nonexistence of exact Lagrangian tori in affine conic bundles over
  4. Automatic epileptic seizure detection via Stein kernel-based sparse representation
  5. Residue formula for an obstruction to coupled Kähler–Einstein metrics
  6. Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds
  7. On matrix pairs with diagonal commutators
  8. Computing square-free polarized abelian varieties over finite fields
  9. Distinguishing open symplectic mapping tori via their wrapped Fukaya categories
  10. A class of structure-preserving discontinuous Galerkin variational time integrators for Birkhoffian systems


  1. A max inequality for spectral invariants of disjointly supported Hamiltonians
  2. A knot Floer stable homotopy type
  4. Projective models of Nikulin orbifolds
  5. Knot probabilities in equilateral random polygons
  6. Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
  7. On -harmonic forms of complete almost K\”{a}hler manifold
  8. An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation
  9. Semisolid sets and topological measures
  10. Weierstrass models


  2. Non-resonant circles for strong magnetic fields on surfaces
  3. Projected exponential Runge–Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems
  4. Deformations of Spacetime Symmetries: Gravity, Group-Valued Momenta, and Non-Commutative Fields
  5. Classification of six-dimensional monotone symplectic manifolds admitting semifree circle actions II
  6. 20 open questions about deformations of compactifiable manifolds
  7. Support -tilting and 2-torsion pairs
  8. A gap theorem for half-conformally flat manifolds
  9. Transverse -holomorphic curves in nearly K\”ahler
  10. Hyperkähler metrics on cotangent bundles of Hermitian symmetric spaces


  1. The Non-contractibility of Closed Geodesics on Finsler ℝ P n
  2. Coarse geometry and Callias quantisation
  3. On the Derivation of Multisymplectic Variational Integrators for Hyperbolic PDEs Using Exponential Functions
  4. Quantum walks simulating non-commutative geometry in the Landau problem
  5. Short-time Fourier transform of the pointwise product of two functions with application to the nonlinear Schr\” odinger equation
  6. Special Lagrangian submanifolds of log Calabi–Yau manifolds
  7. An obstacle for higher regularity of geodesics in the space of Kähler potentials
  8. An introduction to Hilbert schemes of points on ADE singularities
  9. Complex Ball Quotients and New Symplectic 4-manifolds with Nonnegative Signatures
  10. Unstability Correspondence


  1. Real hypersurfaces of the homogeneous nearly Kähler S3× S3 with P-isotropic normal
  2. Symplectic Quantization II: Dynamics of Space–Time Quantum Fluctuations and the Cosmological Constant
  4. The Height Invariant of a Four-Parameter Semitoric System with Two Focus–Focus Singularities
  5. Curves on K3 surfaces in divisibility 2
  6. On the geometric structure of integrable ows in Grassman manifolds
  7. Trisections and Ozsvath-Szabo cobordism invariants
  8. The geometry of marked contact Engel structures
  9. The Roles of Entropy
  10. Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School


  1. Lagrangian Curve Flows on Symplectic Spaces
  2. Double cover K3 surfaces of Hirzebruch surfaces
  3. Two closed orbits for non-degenerate Reeb flows
  4. Resolution à la Kronheimer of C 3 / Γ singularities and the Monge–Ampère equation for Ricci-flat Kähler metrics in view of D3-brane solutions of …
  5. Contact geometry in superconductors and New Massive Gravity
  6. Twisted basic Dolbeault cohomology on transverse K\” ahler foliations
  7. Frobenius Structures and Generalized Deformation of Kodaira Manifolds
  8. On the vibration of moving distributed masses of cantilever shaped-orthotropic rectangular plate resting on constant elastic pasternak foundation
  9. Quantum geometry induced second harmonic generation
  10. Geometric theta-lifting for unitary groups


  1. The relation between the symplectic group and its Lie algebra: its application in polymer quantum mechanics
  2. Minimal Lagrangian tori and action-angle coordinates
  3. Dark Modes in Non-Markovian Linear Quantum Systems
  4. Two Action-Angle Surprises on the Sphere
  5. The geometry of antisymplectic involutions, I
  6. The integrability of symplectic twist maps without conjugate points
  7. Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance
  8. Encyclopedia of Knot Theory
  9. Effective gravitational action for 2D massive fermions
  10. Nonassociative Geometry of Nonholonomic Phase Spaces with Star R‐flux String Deformations and (non) Symmetric Metrics


  1. Homological mirror symmetry for nodal stacky curves
  2. Dimensional reduction in cohomological Donaldson-Thomas theory
  3. Fuerteventura island volume
  4. Optimal Regulators in Geometric Robotics
  5. Analysis of auxetic core sandwich beams subjected to transversely localized loads using two-dimensional symplectic elasticity approach
  6. The “Emerging” Reality from “Hidden” Spaces
  7. Gauge Theory and the Analytic Form of the Geometric Langlands Program
  8. Local structure-preserving algorithms for the molecular beam epitaxy model with slope selection
  10. Haantjes algebras of classical integrable systems


  1. Higher extensions for gentle algebras
  2. Deformations of spacetime symmetries
  3. Free dihedral actions on abelian varieties
  4. The geometry of E-manifolds
  5. Contact Hamiltonian Description of 1D Frictional Systems

Symplectic geometry Research Topics Ideas

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