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

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

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

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

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

47. The John Conway Hour, NTBA
48. Low Dimensional Supersymmetric Gauge Theories and Mathematical Applications
49. A dissipation-preserving scheme for damped oscillatory Hamiltonian systems based on splitting
50. Moduli Spaces of Higgs Bundles–Old and New
51. Scalar curvature and the moment map in generalized Kahler geometry
52. Microscopic shell-model counterpart of the Bohr–Mottelson model
53. Dynamical Quantization of Contact Structures
54. Geometric Numerical Integration (hybrid meeting)
55. Applications of metaplectic cohomology and global-local contact holonomy
56. Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

57. Equivariant and supersymmetric localization in QFT
58. The tools of mechanics by E. Cartan and classical field theory
59. 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 …
60. When scale is surplus
61. Tropical Lagrangians in toric del-Pezzo surfaces
62. Dressing operators in equivariant Gromov-Witten theory of
63. BV and BFV for the H-twisted Poisson sigma model
64. ON THE ROUQUIER DIMENSION OF WRAPPED FUKAYA CATEGORIES
65. The symplectic s-cobordism conjecture: a summary
66. Lectures on Mathematical Methods in Physics

67. Nonassociative analogs of Lie groupoids
68. Non-commutative integrability, exact solvability and the Hamilton–Jacobi theory
69. Generalising G 2 geometry: involutivity, moment maps and moduli
70. Tau function and moduli of meromorphic quadratic differentials
71. Sheaf theoretic compactifications of the space of rational quartic plane curves
72. Superconformal geometries and local twistors
73. Equivariant deformation quantization and coadjoint orbit method
74. Magnetized Kepler manifolds and their quantization
75. Riemann soliton within the framework of contact geometry
76. Solvable Lie algebras and solvmanifolds

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

87. A max inequality for spectral invariants of disjointly supported Hamiltonians
88. A knot Floer stable homotopy type
89. TRANS-SASAKIAN MANIFOLD AND HYPERSURFACE
90. Projective models of Nikulin orbifolds
91. Knot probabilities in equilateral random polygons
92. Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
93. On -harmonic forms of complete almost K\”{a}hler manifold
94. An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation
95. Semisolid sets and topological measures
96. Weierstrass models

97. SYMMETRIES AND REDUCTION PART II–LAGRANGIAN AND HAMILTON-JACOBI PICTURE
98. Non-resonant circles for strong magnetic fields on surfaces
99. Projected exponential Runge–Kutta methods for preserving dissipative properties of perturbed constrained Hamiltonian systems
100. Deformations of Spacetime Symmetries: Gravity, Group-Valued Momenta, and Non-Commutative Fields
101. Classification of six-dimensional monotone symplectic manifolds admitting semifree circle actions II
102. 20 open questions about deformations of compactifiable manifolds
103. Support -tilting and 2-torsion pairs
104. A gap theorem for half-conformally flat manifolds
105. Transverse -holomorphic curves in nearly K\”ahler
106. Hyperkähler metrics on cotangent bundles of Hermitian symmetric spaces

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

117. Real hypersurfaces of the homogeneous nearly Kähler S3× S3 with P-isotropic normal
118. Symplectic Quantization II: Dynamics of Space–Time Quantum Fluctuations and the Cosmological Constant
119. INVOLUTIVE IDEALS DEFINING ALGEBRAIC GRADIENTS OF SOLUTIONS TO NONSTATIONARY HAMILTON-JACOBI EQUATIONS
120. The Height Invariant of a Four-Parameter Semitoric System with Two Focus–Focus Singularities
121. Curves on K3 surfaces in divisibility 2
122. On the geometric structure of integrable ows in Grassman manifolds
123. Trisections and Ozsvath-Szabo cobordism invariants
124. The geometry of marked contact Engel structures
125. The Roles of Entropy
126. Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

127. Lagrangian Curve Flows on Symplectic Spaces
128. Double cover K3 surfaces of Hirzebruch surfaces
129. Two closed orbits for non-degenerate Reeb flows
130. 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 …
131. Contact geometry in superconductors and New Massive Gravity
132. Twisted basic Dolbeault cohomology on transverse K\” ahler foliations
133. Frobenius Structures and Generalized Deformation of Kodaira Manifolds
134. On the vibration of moving distributed masses of cantilever shaped-orthotropic rectangular plate resting on constant elastic pasternak foundation
135. Quantum geometry induced second harmonic generation
136. Geometric theta-lifting for unitary groups

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

147. Homological mirror symmetry for nodal stacky curves
148. Dimensional reduction in cohomological Donaldson-Thomas theory
149. Fuerteventura island volume
150. Optimal Regulators in Geometric Robotics
151. Analysis of auxetic core sandwich beams subjected to transversely localized loads using two-dimensional symplectic elasticity approach
152. The “Emerging” Reality from “Hidden” Spaces
153. Gauge Theory and the Analytic Form of the Geometric Langlands Program
154. Local structure-preserving algorithms for the molecular beam epitaxy model with slope selection
155. TWISTED JACOBI VERSUS JACOBI WITH BACKGROUND STRUCTURES
156. Haantjes algebras of classical integrable systems

157. Higher extensions for gentle algebras
158. Deformations of spacetime symmetries
159. Free dihedral actions on abelian varieties
160. The geometry of E-manifolds
161. Contact Hamiltonian Description of 1D Frictional Systems

Symplectic geometry Research Topics Ideas