Symplectic geometry Research Topics Ideas

By: Prof. Dr. Fazal Rehman | Last updated: February 3, 2024

1. Coisotropic Submanifolds in b-symplectic Geometry 2. Quantum field theory, equivariant cohomology, symplectic geometry and moduli spaces of vector bundles on Riemann surfaces 3. The symplectic geometry of higher Auslander algebras: Symmetric products of disks 4. Applications of Grothendieck’s inequality to linear symplectic geometry 5. List of exercises of the course” Geometry and Dynamics of Singular Symplectic manifolds” 6. A noise reduction method based on adaptive weighted symplectic geometry decomposition and its application in early gear fault diagnosis 7. Formation of the New Multi-sender Authentication Codes Via Symplectic Space through Finite Commutative Rings with Applications 8. Symplectic, Poisson, and contact geometry on scattering manifolds 9. Symmetry and Symplectic Reduction 10. Holomorphic Curve Theories in Symplectic Geometry 11. Symplectic diffeomorphisms and Weinstein 1-form 12. Time-dependent Hamiltonian mechanics on a locally conformal symplectic manifold 13. Lectures on Poisson Geometry 14. Symplectic microgeometry, IV: Quantization 15. Extended retraction maps: a seed of geometric integrators 16. Geometric Quantization 17. Higher index symplectic capacities do not satisfy the symplectic Brunn-Minkowski inequality 18. Symplectic invariants of semitoric systems and the inverse problem for quantum systems 19. The formal moment map geometry of the space of symplectic connections 20. Symplectic Novikov Lie Algebra 21. Legendre and Isotropic Submanifolds in Contact and Riemannian Geometry with Modern Developments 22. Symplectic reduction along a submanifold 23. An intelligent fault diagnosis method for roller bearing using symplectic hyperdisk matrix machine 24. A general symplectic scheme with three free parameters and its applications 25. Fidelity and mistaken identity for symplectic quantum states 26. Gaussian quantum states can be disentangled using symplectic rotations 27. Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type 28. On the symplectic superposition method for analytic free vibration solutions of right triangular plates 29. New applications of symplectic topology in several complex variables 30. Special Issue “Affine differential geometry and Hesse geometry: a tribute and memorial to Jean–Louis Koszul” 31. Algorithmic Symplectic Packing 32. Generating functions in symplectic and contact geometry 33. Geometric Structures of Statistical Physics, Information Geometry, and Learning 34. DERIVED ALGEBRAIC GEOMETRY 35. The geometry of Rayleigh dissipation 36. Homotopy principle in analysis and geometry 37. No symplectic-Lipschitz structures on 38. On geometric quantization of bm -symplectic manifolds 39. Symplectic quaternion singular mode decomposition with application in gear fault diagnosis 40. Phase Space on a Surface with Boundary via Symplectic Reduction 41. Berezin-Toeplitz quantization on symplectic manifolds of bounded geometry 42. The symplectic geometry of higher Auslander algebras: Symmetric products of disks, Forum of Mathematics 43. Souriau Entropy based on Symplectic Model of Statistical Physics: three Jean-Marie Souriau’s seminal papers on Lie Groups Thermodynamics 44. Poisson structures of near-symplectic manifolds and their cohomology 45. Deformation quantization via Toeplitz operators on geometric quantization in real polarizations 46. Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric 47. Statistics and learning on Lie groups: Information geometry by Jean-Louis Koszul and symplectic model of statistical physics by Jean-Marie Souriau 48. Examples of symplectic non-leaves 49. Symplectic Gaussian process regression of maps in Hamiltonian systems 50. GEOMETRY OF ANOSOV SYSTEMS: AN INTRODUCTION 51. SYMPLECTIC MECHANICS AND DIFFEOLOGY 52. Picard groups of -symplectic manifolds 53. Real and complex hedgehogs, their symplectic area, curvature and evolutes 54. Kenji Fukaya 55. Equivariant Seidel maps and a flat connection on equivariant symplectic cohomology 56. A semi-analytical model for the modal density of periodic mediums based on the symplectic method 57. Lagrangian Curve Flows on Symplectic Spaces. Symmetry 2021, 13, 298 58. A Symplectic Conservative Perturbation Series Expansion Method for Linear Hamiltonian Systems with Perturbations and Its Applications 59. BPS States as Symplectic Invariants from String Theory 60. On the complex structure of symplectic quotients 61. Quantum cohomology of symplectic flag manifolds 62. Characteristic equation for symplectic groupoid and cluster algebras 63. Realizability and Obstruction in Tropical Geometry 64. Resolution of four-dimensional symplectic orbifolds 65. Some algebraic and geometric aspects of quantum measurements 66. The Globalization Problem of the Hamilton–DeDonder–Weyl Equations on a Local k-Symplectic Framework 67. The invariants of planar 3-webs with respect to group of symplectic diffeomorphisms, for the case of the conformal group 68. Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids 69. Reconstruction of holomoprhic tangent bundle of complex projective plane via tropical Lagrangian multi-section 70. A Fourth Order Symplectic and Conjugate-Symplectic Extension of the Midpoint and Trapezoidal Methods 71. Positivity-preserving symplectic methods for the stochastic Lotka–Volterra predator-prey model 72. Extended retraction maps: a seed of geometric integrators 73. Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang 74. Geometric quantization of symplectic maps and Witten’s asymptotic conjecture 75. QUANTIZATION OF SYMPLECTIC COBORDISMS 76. Operad Structures in Geometric Quantization of the Polygon Spaces 77. Symplectic 4‐manifolds admit Weinstein trisections 78. Stabilized convex symplectic manifolds are Weinstein 79. On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties 80. Towards a quantization of the double via the enhanced symplectic “category” 81. Archetypal Model of Entropy as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation 82. Berezin-Toeplitz Quantization in Real Polarizations with Toric Singularities 83. The Replicator Dynamics of Zero-Sum Games Arise from a Novel Poisson Algebra 84. Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and Geometric Fourier Heat Equation 85. CP symmetry and symplectic modular invariance 86. Local mirror symmetry via SYZ 87. Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization 88. Local geometry of symplectic divisors with applications to contact torus bundles 89. Subcritical polarisations of symplectic manifolds have degree one 90. New geometrical and dynamical techniques for problems in celestial mechanics 91. Semisymplectic group and Hamiltonian vector fields 92. The second-order problem for -presymplectic Lagrangian field theories. Application to the Einstein–Palatini model 93. Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kähler geometry 94. Symplectic integration of learned Hamiltonian systems 95. Special Bohr-Sommerfeld geometry: variations 96. On symplectic automorphisms of elliptic surfaces acting on 97. On forms, cohomology and BV Laplacians in odd symplectic geometry 98. Symplectic geometry and connectivity of spaces of frames 99. Derived stacks in symplectic geometry 100. Dusa McDuff and symplectic geometry 101. Symplectic geometry of a moduli space of framed Higgs bundles 102. Quantitative -principle in symplectic geometry 103. Structure Topology and Symplectic Geometry 104. Twistor operators in symplectic geometry 105. First steps into the world of systolic inequalities: From Riemannian to symplectic geometry 106. A novel fault diagnosis procedure based on improved symplectic geometry mode decomposition and optimized SV 107. Chekanov-Eliashberg dg-algebras and partially wrapped Floer cohomology 108. Classification of real simple symplectic triple systems 109. Kaldor–Kalecki New Model on Business Cycles 110. Cohomology of Quotients in Symplectic and Algebraic Geometry.(MN-31), Volume 31 111. Quantization via integrable systems 112. A Review Note on the Applications of Linear Operators in Hilbert Space 113. Persistence in functional topology and a correction to a theorem of Morse 114. On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge 115. Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles 116. Viva Fukaya! 117. A Novel Signature Extracting Approach for Inductive Oil Debris Sensors based on Symplectic Geometry Mode Decomposition 118. Application of Improved Symplectic Geometry Mode Decomposition Algorithm in Evaluation System of Transformer Winding Short‐Circuit Withstand Ability 119. New Spaces in Mathematics: Formal and Conceptual Reflections 120. Maximum envelope-based autogram and symplectic geometry mode decomposition based gear fault diagnosis method 121. Fast symplectic integrator for Nesterov-type acceleration method 122. Quantum cohomology as a deformation of symplectic cohomology 123. Conformal symplectic structures, contact topology, and foliations 124. Symplectic structure of equilibrium thermodynamics 125. On dissipative symplectic integration with applications to gradient-based optimization 126. Coarse-graining and symplectic non-squeezing 127. Shifted symplectic reduction of derived critical loci 128. Experimental Comparison of Symplectic and Non-symplectic Model Order Reduction on an Uncertainty Quantification Problem 129. Open Problems in Global Analysis. Structured Foliations and the Information Geometry 130. Symplectic -manifolds 131. Holomorphic Curve Theories in Symplectic Geometry 132. Hamilton–Jacobi formalism on locally conformally symplectic manifolds 133. SYMPLECTIC Zn 2-MANIFOLDS 134. Convexity In Contact Geometry And Reeb Dynamics 135. Koszul lecture related to geometric and analytic mechanics, Souriau’s Lie group thermodynamics and information geometry 136. Symplectic Novikov Lie Algebra 137. Closed orbits of Reeb fields on compact Sasakian manifolds 138. Integrable Hamiltonian systems on the symplectic realizations of 139. Quantum Mechanics as Hamilton-Killing Flows on a Statistical Manifold 140. Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method 141. Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics 142. On the stopping distance of LDPC codes based on symplectic space over finite fields 143. On a deformed version of the two-disk dynamo system 144. Twisted cotangent bundle of Hyperkähler manifolds (with an appendix by Simone Diverio) 145. Symplectic Homology and Shape of Cotangent Bundles 146. Invariant manifolds in Hamiltonian systems with applications to the Earth-Moon system 147. Analysis on Boundary Conditions for Elastic Structures 148. Symplectic resolutions of quiver varieties 149. Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps 150. Exponential sums and total Weil representations of finite symplectic and unitary groups 151. Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties 152. Pseudo-rotations and symplectic topology 153. Geometric quantization and non-perturbative Poisson sigma model 154. foliations for Reeb flows on the tight 3-sphere 155. Anti-symplectic involutions for Lagrangian spheres in a symplectic quadric surface 156. Uniqueness of optimal symplectic connections 157. Some algebraic and geometric constructions in quantum information theory 158. Matched pair analysis of the Vlasov plasma 159. Advanced course in classical and quantum chaos 160. Maximal Page Crossing Numbers of Legendrian Surfaces in Closed Contact 5-Manifolds 161. Asymptotic behavior of exotic Lagrangian tori in as 162. NON-SYMPLECTIC INVOLUTIONS ON MANIFOLDS OF-TYPE 163. Basic facts and naive questions 164. A Lorentzian distance function for positive contactomorphisms 165. MATH 703: PART 4: INTEGRAL CURVES AND FLOWS 166. Sturm theory with applications in geometry and classical mechanics 167. Gerbes in Geometry, Field Theory, and Quantisation 168. Gaussian Distributions on the Space of Symmetric Positive Definite Matrices from Souriau’s Gibbs State for Siegel Domains by Coadjoint Orbit and Moment Map 169. Regularity of Hamiltonian Stationary Equations in Symplectic manifolds 170. Elena Cordero and Luigi Rodino:“Time-Frequency Analysis of Operators” 171. Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization 172. Invariant Koszul form of homogeneous bounded domains and information geometry structures 173. The action spectrum and C 0 symplectic topology 174. On the existence of universal families of marked irreducible holomorphic symplectic manifolds 175. An algebraic approach to the algebraic Weinstein conjecture 176. Symplectic 4-manifolds with b 2+= 1 177. Symplectic Dirac cohomology and lifting of characters to metaplectic groups 178. NATURAL SYMPLECTIC STRUCTURES ON THE TANGENT BUNDLE OF A SPACE {TIME 179. Two Perspectives on the Local Symplectic Homology of Closed Reeb Orbits 180. On Euler number of symplectic hyperbolic manifold 181. Geometry of the space of sections of twistor spaces with circle action 182. Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole 183. Varieties of minimal rational tangents of unbendable rational curves subordinate to contact structures 184. A NOVEL WAY CONSTRUCTING SYMPLECTIC STOCHASTIC PARTITIONED RUNGE-KUTTA METHODS FOR STOCHASTIC HAMILTONIAN SYSTEMS 185. Uniqueness of exact Borel subalgebras and bocses 186. Integrability of point-vortex dynamics via symplectic reduction: a survey 187. The Complex Geometry and Representation Theory of Statistical Transformation Models 188. Quantization: Crossroads and Crossovers 189. Noncommutative homological mirror functor 190. Extendable symplectic structures and the inverse problem of the calculus of variations for systems of equations written in generalized Kovalevskaya form 191. Admissibility and Frame Homotopy for Quaternionic Frames 192. a review of A categorical approach to quantum moment maps by Safronov, Pavel 193. Controllability Study on the Symplectic Lie Group Sp (2, R) 194. Liouville geometry of classical thermodynamics 195. Symmetries, constants of the motion, and reduction of mechanical systems with external forces 196. Noncommutative coordinate picture of the quantum phase space 197. Asymptotic Dynamics of Hamiltonian Polymatrix Replicators 198. KSBA compactification of the moduli space of K3 surfaces with a purely non-symplectic automorphism of order four 199. Higher dimensional Lie algebroid sigma model with WZ term 200. Analytic embedding of pseudo-Helmholtz geometry 201. Geometry of complex instability and escape in four-dimensional symplectic maps 202. Categorical mirror symmetry on cohomology for a complex genus 2 curve (vol 375, 107392, 2021) 203. On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms 204. Symplectic fillings, contact surgeries, and Lagrangian disks 205. Explicit, time-reversible and symplectic integrator for Hamiltonians in isotropic uniformly curved geometries 206. Supersymmetric Hyperbolic σ -Models and Bounds on Correlations in Two Dimensions 207. Geometric quantization via cotangent models 208. Towards a T-dual Emergent Gravity 209. Linearization of Poisson groupoids 210. Residues and obstructions for log-symplectic manifolds 211. Contact Dynamics versus Legendrian and Lagrangian Submanifolds 212. Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back 213. Deformations of rational curves on primitive symplectic varieties and applications 214. Laplace eigenfunctions on Riemannian symmetric spaces and Borel-Weil Theorem 215. An Extension of Greene’s Criterion for Conformally Symplectic Systems and a Partial Justification 216. Beyond Conventional Quantum Mechanics 217. On symplectic fillings of virtually overtwisted torus bundles 218. Non-formal contact manifolds with 219. Variational Symplectic Accelerated Optimization on Lie Groups 220. Mini-Workshop: Superpotentials in Algebra and Geometry 221. Hopf–Cole transformation via generalized Schrödinger bridge problem 222. Categorical action filtrations via localization and the growth as a symplectic invariant 223. Boucksom-Zariski and Weyl chambers on irreducible holomorphic symplectic manifolds 224. Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps 225. The tropical symplectic Grassmannian 226. Derived equivalences for Symplectic reflection algebras 227. The AKSZ construction in derived algebraic geometry as an extended topological field theory 228. of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics-Quod Erat Demonstrandum 229. On Submanifolds and Deformations in Poisson Geometry 230. Archetypal Model of Entropy by Poisson Cohomology as Invariant Casimir Function in Coadjoint Representation and… 231. Moonshine at Landau-Ginzburg points 232. The geometry and topology of steady Euler flows, integrability and singular geometric structures 233. Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries 234. The geometry and topology of steady Euler flows, integrability and singular geometric structures 235. On -harmonic forms of symplectic hyperbolic manifold 236. The rectangular peg problem 237. Conformal symplectic Weinstein conjecture and non-squeezing 238. Volume and symplectic structure for ℓ-adic local systems 239. Symplectic resolutions of the quotient of R^ 2 by a non-finite symplectic group 240. … 2020, FOR’A BOGOMOLOV UNOBSTRUCTEDNESS THEOREM FOR LOG-SYMPLECTIC MANIFOLDS IN GENERAL POSITION'(J. INST. MATH. JUSSIEU 19 (2018) … 241. Classification of Holomorphic Functions as Pólya Vector Fields via Differential Geometry 242. Automated synthesis of contextuality proofs from subspaces of symplectic polar spaces 243. On new analytic free vibration solutions of doubly curved shallow shells by the symplectic superposition method within the Hamiltonian-system framework 244. Symplectic Transformations on Wigner Distributions and Time Frequency Signal Design 245. Family Floer theory of toric manifolds and wall-crossing phenomenon 246. Sharpness of Seeger-Sogge-Stein orders for the weak (1, 1) boundedness of Fourier integral operators 247. Convergence and Riemannian bounds on Lagrangian submanifolds 248. Compactifying torus fibrations over integral affine manifolds with singularities 249. Lagrangian fields, Calabi functions, and local symplectic groupoids 250. An Overview of the Hamilton–Jacobi Theory: the Classical and Geometrical Approaches and Some Extensions and Applications 251. Scale Symmetry and Friction 252. Binary Subspace Chirps 253. Donaldson–Thomas theory of Calabi–Yau 3-folds 254. On 2-plectic Lie groups 255. Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping 256. Quantum cohomology as a deformation of symplectic cohomology 257. Examples of Mironov Cycles in Grassmannians 258. Classical BV formalism for group actions 259. Products of positive definite symplectic matrices 260. Geometry in dg-categories 261. Frobenius Statistical manifolds, Geometric invariants & Hidden symmetries 262. Absolute points of correlations of PG ( 3 , qn ) 263. String Topology and Cyclic Homology 264. Covariant momentum map thermodynamics for parametrized field theories 265. Homological mirror symmetry at large volume 266. Special solutions to the Type IIA flow 267. Bounds on subspace codes based on subspaces of type (s, 0, 0, 0) in pseudo-sympletic spaces and singular pseudo-symplectic spaces 268. Complexified Hermitian Symmetric Spaces, Hyperk\” ahler Structures, and Real Group Actions 269. Dirac structures on the space of connections 270. Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory 271. On the modified least action principle with dissipation 272. Frobenius objects in the category of spans 273. On the moduli spaces of framed logarithmic connections on a Riemann surface 274. a review of Odd connections on supermanifolds: existence and relation with affine connections by Bruce, Andrew James (LUX-ULUX2-MRU); Grabowski, Janusz (PL … 275. New stick number bounds from random sampling of confined polygons 276. Mathematical Structures in Physics 277. Testing Quantum Contextuality of Binary Symplectic Polar Spaces on a Noisy Intermediate Scale Quantum Computer 278. On new buckling solutions of moderately thick rectangular plates by the symplectic superposition method within the Hamiltonian-system framework 279. The singular Weinstein conjecture 280. Equivariant prequantization and the moment map 281. The CR geometry of weighted extremal Kähler and Sasaki metrics 282. Conformal Hamiltonian Mechanical Equations on Contact 9-Manifolds 283. Calabi-Yau structures for multiplicative preprojective algebras 284. A Cartan-Hartogs version of the Polydisk Theorem 285. Четырехмерные однородные пространства с почти симплектической структурой. Комплексный случай 286. Workshop on geometry in algebra and algebra in geometry 287. Geometric formulation of the Covariant Phase Space methods with boundaries 288. Thermodynamic identities with sunray diagrams 289. Batalin-Vilkovisky Quantisation of Bosonic Strings Revisited 290. The Abelian/non-Abelian Correspondence and Gromov-Witten Invariants of Blow-ups 291. Seizure Detection Based on Adaptive Feature Extraction by Applying Extreme Learning Machines. 292. Spiraling of sub-Riemannian geodesics around the Reeb flow in the 3D contact case 293. Uniqueness properties of the KAM curve 294. Deformation theory of orthogonal and symplectic sheaves 295. Seminar on the h-principle 296. Gromov-Hausdorff distance between filtered categories 1: Lagrangian Floer theory 297. New action for cosmology 298. Formulation of stochastic contact Hamiltonian systems 299. An Algebraic-Geometric Characterization of Tripartite Entanglement 300. A four-dimensional mapping class group relation 301. Factorization Algebras for Bulk-Boundary Systems 302. Quantum Orbit Method in the Presence of Symmetries 303. On Hausdorff integrations of Lie algebroids 304. Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry 305. New analytic buckling solutions of side-cracked rectangular thin plates by the symplectic superposition method 306. A local normal form for Hamiltonian actions of compact semisimple Poisson-Lie groups 307. Jean-Louis Koszul, Julien Koszul & Mathieu Koszul: From Poniatowski Grande Armée of Napoleon to Bourbaki Group 308. On Symmetric Brackets Induced by Linear Connections 309. Complex Dirac structures: invariants and local structure 310. Curved Yang–Mills-Higgs gauge theories in the case of massless gauge bosons 311. On the uniqueness of invariant states 312. On the iterated Hamiltonian Floer homology 313. The weak (1, 1) type of Fourier integral operators with complex phases 314. J. Adv. Math. Stud. 315. Legendrian Satellites and Decomposable Cobordisms 316. Stochastic symplectic ice 317. Reeb flow invariant∗-Ricci operators on trans-Sasakian three-manifolds 318. Symplectic excision 319. Propagation of singularities for subelliptic wave equations 320. Topological and dynamical aspects of Jacobi sigma models 321. Optimal Four-Stage Symplectic Integrators for Molecular Dynamics Problems 322. Quantum Systems as Lie Algebroids 323. Construction of Explicit Symplectic Integrators in General Relativity. II. Reissner–Nordström Black Holes 324. Commuting symplectomorphisms on a surface and the flux homomorphism 325. A long-term numerical energy-preserving analysis of symmetric and/or symplectic extended RKN integrators for efficiently solving highly oscillatory Hamiltonian … 326. The Hamilton–Jacobi theory for contact Hamiltonian systems 327. An energy gap phenomenon for the Whitney sphere 328. On the geometry of discrete contact mechanics 329. Manifolds of isospectral arrow matrices 330. Williamson theorem in classical, quantum, and statistical physics 331. Sub-Riemannian (2, 3, 5, 6)-Structures 332. The Gopakumar-Vafa finiteness conjecture 333. Topology, Geometry, and Dynamics: VA Rokhlin-Memorial 334. On local geometry of rank 3 distributions with 6-dimensional square 335. Dehn-Seidel twist, symplectic topology and barcodes 336. Geometric structure of generalised gauge field theories 337. Lie groups of Poisson diffeomorphisms 338. A k-contact Lagrangian formulation for nonconservative field theories 339. Towards an extended/higher correspondence–Generalised geometry, bundle gerbes and global Double Field Theory 340. Free-Boundary Problems for Holomorphic Curves in the 6-Sphere 341. A note on the structure of prescribed gradient–like domains of non–integrable vector fields 342. Double field theory and geometric quantisation 343. Quasienergy operators and general squeezed states for systems of trapped ions 344. Hermitian Symmetric Spaces for Graph Embeddings 345. Volume-Preserving Diffeomorphisms with the M 0 -Shadowing Properties 346. A Gutzwiller trace formula for stationary space-times 347. Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations 348. Hamiltonian charges in the asymptotically de Sitter spacetimes 349. An analytic application of Geometric Invariant Theory 350. A Hyperk\” ahler geometry associated to the BPS structure of the resolved conifold 351. Energy-Constrained Discrimination of Unitaries, Quantum Speed Limits, and a Gaussian Solovay-Kitaev Theorem 352. The d-critical structure on the Quot scheme of points of a Calabi-Yau 3-fold 353. Some examples of stable generalized complex 6-manifolds with either 0 or negative Euler characteristic 354. Guia docent 34966-VD-Varietats Diferenciables 355. Matched Pair Analysis of Euler-Poincar\'{e} Flow on Hamiltonian Vector Fields 356. Riemannian optimization on the symplectic Stiefel manifold 357. Minimal Lagrangian surfaces in ℂP2 via the loop group method Part I: The contractible case 358. Derived invariance of Crawley-Boevey’s -Poisson structure 359. Gopakumar–Vafa type invariants on Calabi–Yau 4-folds via descendent insertions 360. Morse-Smale characteristic foliations and convexity in contact manifolds 361. Complex vs convex Morse functions and geodesic open books 362. A contact camel theorem 363. Modeling of seizure and seizure-free EEG signals based on stochastic differential equations 364. Jacobi Multipliers in Integrability and the Inverse Problem of Mechanics 365. Mechanoelectrical flexible hub-beam model of ionic-type solvent-free nanofluids 366. Symplectic neural networks in Taylor series form for Hamiltonian systems 367. A Gentle Introduction to Homological Mirror Symmetry 368. Symplectic Topology in the cotangent bundle through Generating functions 369. Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials 370. High order explicit Lorentz invariant volume-preserving algorithms for relativistic dynamics of charged particles 371. Double field theory and geometric quantisation 372. A closing lemma on torus 373. NOTES ON MONODROMY AND PARALLEL TRANSPORT OF HOLOMORPHIC-SYMPLECTIC VARIETIES OF K3 [n]-TYPE 374. Noise effects on the Wilczek–Zee geometric phase 375. Anomalies in gravitational charge algebras of null boundaries and black hole entropy 376. Finite quotients of surface braid groups and double Kodaira fibration 377. A Gentle Introduction to Homological Mirror Symmetry 378. Symplectic Topology in the cotangent bundle through Generating functions 379. Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials 380. High order explicit Lorentz invariant volume-preserving algorithms for relativistic dynamics of charged particles 381. Double field theory and geometric quantisation 382. A closing lemma on torus 383. NOTES ON MONODROMY AND PARALLEL TRANSPORT OF HOLOMORPHIC-SYMPLECTIC VARIETIES OF K3 [n]-TYPE 384. Noise effects on the Wilczek–Zee geometric phase 385. Anomalies in gravitational charge algebras of null boundaries and black hole entropy 386. Finite quotients of surface braid groups and double Kodaira fibrations 387. Segal-Bargmann transforms from hyperbolic Hamiltonians 388. An Introduction to Orthogonal Geometry 389. Spin Matrix theory string backgrounds and Penrose limits of AdS/CFT 390. Spectral asymptotics on stationary space-times 391. From Schouten to Mackenzie: notes on brackets 392. Poisson gauge theory 393. What do we need to build up Quantum Mechanics on Manifolds? The Lecture given at the Mathematical Institute of the Oslo University, 21.03. 96 394. Simultaneous preservation of two or more geometric properties, Network wide training course 6 395. Hamiltonian structure for a differential system from a modified Laguerre weight via the geometry of the modified third Painlevé equation 396. Fano Varieties of K3-Type and IHS Manifolds 397. Local unitary classification of generalized Bell state sets in 398. Open systems in classical mechanics 399. Harish-Chandra bimodules over quantized symplectic singularities 400. On a remark by Ohsawa related to the Berndtsson-Lempert method for -holomorphic extension 401. Noncommutative Poisson vertex algebras and Courant-Dorfman algebras 402. Theory and modeling of a novel class of nanoplate-based mass sensors with corner point supports 403. Disjoint superheavy subsets and fragmentation norms 404. Covariant phase space and soft factorization in non-Abelian gauge theories 405. Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic … 406. Transverse hilbert schemes, bi-hamiltonian systems and hyperkähler geometry 407. Tuning symplectic integrators is easy and worthwhile 408. From Newton to Hamilton, bypassing Lagrange and Legendre. 409. Lifting of the Action of Symplectomorphism Group on the Bi-Lagrangian Structure 410. The Traverse Symplectic Correlation-Gram (TSCgram): A New and Effective Method of Optimal Demodulation Band Selection for Rolling Bearing 411. Sections of Hamiltonian Systems 412. Towers of Looijenga pairs and asymptotics of ECH capacities 413. Z-graded supergeometry: Differential graded modules, higher algebroid representations, and linear structures 414. Affine hypersurfaces of arbitrary signature with an almost symplectic form 415. New quiver-like varieties and Lie superalgebras 416. Symplectic embeddings of the ℓ p-sum of two discs 417. Tuning symplectic integrators is easy and worthwhile 418. From Newton to Hamilton, bypassing Lagrange and Legendre. 419. Lifting of the Action of Symplectomorphism Group on the Bi-Lagrangian Structure 420. The Traverse Symplectic Correlation-Gram (TSCgram): A New and Effective Method of Optimal Demodulation Band Selection for Rolling Bearing 421. Sections of Hamiltonian Systems 422. Towers of Looijenga pairs and asymptotics of ECH capacities 423. Z-graded supergeometry: Differential graded modules, higher algebroid representations, and linear structures 424. Affine hypersurfaces of arbitrary signature with an almost symplectic form 425. New quiver-like varieties and Lie superalgebras 426. Symplectic embeddings of the ℓ p-sum of two discs 427. Goldman form, flat connections and stable vector bundles 428. Systolic inequalities for K3 surfaces via stability conditions 429. Order-corrected symplectic finite element method for elastic wave modelling 430. Contact Hamiltonian Systems for Probability Distribution Functions and Expectation Variables: A Study Based on a Class of Master Equations 431. The Calabi invariant for Hamiltonian diffeomorphisms of the unit disk 432. On the Δ -property for complex space forms 433. Stability conditions in families 434. Complexity for Conformal Field Theories in General Dimensions 435. Factorization algebras in quantum field theory 436. Shearing deformations of Hitchin representations and the Atiyah–Bott–Goldman symplectic form 437. Euler continuants in noncommutative quasi-Poisson geometry 438. Poisson structure on character varieties 439. Elastoplastic nonlinear analysis of functionally graded beams utilizing the symplectic method 440. The Deformed Hermitian-Yang-Mills Equation with Calabi Ansatz 441. Algebraic cycles and Lehn-Lehn-Sorger-van Straten eightfolds 442. Stable pairs and Gopakumar–Vafa type invariants for Calabi–Yau 4-folds 443. New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method 444. Entropy, holography, and p-adic geometry 445. A primer on the differential geometry of quaternionic curves 446. A simplicial version of the 2-dimensional Fulton-MacPherson operad 447. Quantization of Kähler manifolds 448. Deep Learning: Hydrodynamics, and Lie-Poisson Hamilton-Jacobi Theory 449. Mixing rates for symplectic almost Anosov maps 450. Classical Invariants of Legendrian and Transverse Knots 451. On two geometric means and sum of adjoint orbits 452. New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework 453. Many closed K -magnetic geodesics on S 2 454. Castelnuovo’s bound and rigidity in almost complex geometry 455. Corks, covers, and complex curves 456. Infinitesimally tight Lagrangian orbits 457. Spine removal surgery and the geography of symplectic fillings 458. Topological aspects of incompressible flows 459. Generalized and graded geometry for mechanics: a comprehensive introduction 460. A geometric approach to Lie systems: formalism of Poisson-Hopf algebra deformations 461. The Gromov width of generalized Bott manifolds 462. Computation of quantum cohomology from Fukaya categories 463. Quantization of dynamical symplectic reduction 464. Singularities in one-dimensional Euler flows 465. Geodesic of the Quotient-Affine Metrics on Full-Rank Correlation Matrices 466. Quantization of canonical bases and the quantum symplectic double 467. Black holes and the swampland: the deep throat revelations 468. Koopman wavefunctions and Clebsch variables in Vlasov-Maxwell kinetic theory 469. A natural topological manifold structure of phase tropical hypersurfaces 470. Symplectic groups over noncommutative algebras 471. Dynamical reduced basis methods for Hamiltonian systems 472. Order 3 symplectic automorphisms on K3 surfaces 473. Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds 474. Distortion of the Poisson Bracket by Noncommutative Planck Constants 475. A double copy for asymptotic symmetries in the self-dual sector 476. Partial geometric designs having circulant concurrence matrices 477. Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants 478. Frobenius Statistical Manifolds and Geometric Invariants 479. Singularities, Mirror Symmetry, and the Gauged Linear Sigma Model 480. Superintegrability of Generalized Toda Models on Symmetric Spaces 481. Transport barriers in symplectic maps 482. Some Classification Results for Symplectic Fillings of Contact 3-Manifolds 483. Effects of local thinning defects and stepped thickness for free vibration of cylindrical shells using a symplectic exact solution approach 484. The integrability of Virasoro charges for axisymmetric Killing horizons 485. An adjunction inequality for the Bauer-Furuta type invariants, with applications to sliceness and 4-manifold topology 486. Wind power forecasting based on stacking ensemble model, decomposition and intelligent optimization algorithm 487. SPECIAL GEOMETRY ON THE MODULI SPACE OF THE CALABI-YAU THREEFOLDS 488. -gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces 489. A geometric approach to the generalized Noether theorem 490. Poisson Yang-Baxter equations and -operators of Poisson superalgebras 491. Singularities of Solutions of Hamilton–Jacobi Equations 492. A decoupling property of some Poisson structures on supporting Poisson–Lie symmetry 493. Relative growth rate and contact Banach–Mazur distance 494. Kähler fibrations in quantum information theory 495. The openness condition for a coadjoint orbit projection of the semidirect product Lie group M ((n, p), ℝ)⋊ GL (n, ℝ) 496. A semi-theoretical method to detect classical monodromy 497. D-critical loci for local toric Calabi-Yau 3-folds 498. Deformation quantization via Toeplitz operators on geometric quantization in real polarizations 499. Algebroids, AKSZ Constructions and Doubled Geometry 500. Geometric numerical integration of differential equations, THREAD Network-wide training event 6 501. Fukaya categories of higher-genus surfaces and pants decompositions 502. and Applications 503. First Steps in Twisted Rabinowitz-Floer Homology 504. Deformation quantization of moduli spaces of Higgs bundles on a Riemann surface with translation structure 505. Concise symplectic formulation for tetrad gravity 506. Some New Results in Geometric Analysis 507. Discrete linear canonical evolution 508. KONTSEVICH GRAPHONS 509. Theory of Symplectic Twist Maps applied to Point-vortex Dynamics 510. Gravitating vortices and the Einstein–Bogomol’nyi equations 511. نگاشت تکانی k-تایی‎ 512. Symplectic fillings of asymptotically dynamically convex manifolds I 513. Efficient linearized local energy-preserving method for the Kadomtsev-Petviashvili equation 514. On stabiliser techniques and their application to simulation and certification of quantum devices 515. Positive Exponents for Random Products of Conservative Surface Diffeomorphisms and Some Skew Products 516. COMPACTNESS RESULTS FOR HOLOMORPHIC CURVES 517. Critical Phenomena in Darcy and Euler Flows of Real Gases 518. Integrability, normal forms, and magnetic axis coordinates 519. Invitation: Gravity, Point Particles, and Group-Valued Momenta 520. A canonical connection on bundles on Riemann surfaces and Quillen connection on the theta bundle 521. Topological Light–Matter Design: Simulations in Polariton Profiles and Ultracold Atom Systems 522. On curvature and torsion in Courant algebroids 523. Quantum (non-commutative) toric geometry: foundations 524. Quantization of canonical bases and the quantum symplectic double 525. Mayer–Vietoris property for relative symplectic cohomology 526. Spectra of Tensor Triangulated Categories over a Category Algebra—A New Approach 527. Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory 528. On degenerations and extensions of symplectic and orthogonal quiver representations 529. Analytical solution of the electro-mechanical flexural coupling between piezoelectric actuators and flexible-spring boundary structure in smart composite plates 530. On the tensor semigroup of affine kac-moody lie algebras 531. Quantum Harmonic Analysis: An Introduction 532. The Faber-Krahn inequality for the Short-time Fourier transform 533. Applications of Digital Signal Processing in Monitoring Machining Processes and Rotary Components: A Review 534. A new Quantum Mechanics on phase space 535. A categorical approach to quantum moment maps 536. Brane current algebras and generalised geometry from QP manifolds 537. Arborealization I: Stability of arboreal models 538. Optimization, Complexity and Invariant Theory (Invited Talk) 539. Central extensions of Lie groups preserving a differential form 540. Products and connected sums of spheres as monotone Lagrangian submanifolds 541. Real structures on nilpotent orbit closures 542. On the Hodge and Betti numbers of hyper-Kähler manifolds 543. Three-Dimensional Mirror Symmetry and Elliptic Stable Envelopes 544. Eigenfunctions expansion for discrete symplectic systems with general linear dependence on spectral parameter 545. A note on multi-oriented graph complexes and deformation quantization of Lie bialgebroids 546. Extremal length in higher dimensions and complex systolic inequalities 547. The category of weight modules for symplectic oscillator Lie algebras 548. Contact Hamiltonian dynamics and perturbed contact instantons with Legendrian boundary condition 549. An introduction to the topology of the moduli space of stable bundles on a Riemann surface 550. Theory of homotopes with applications to mutually unbiased bases, harmonic analysis on graphs, and perverse sheaves 551. Keplerian orbits through the Conley–Zehnder index 552. Singular geometrical optics for differential operators on surfaces 553. Conserved momenta of ferromagnetic solitons through the prism of differential geometry 554. The coordinate algebra of a quantum symplectic sphere does not embed into any C*-algebra 555. Understanding Quaternions from Modern Algebra and Theoretical Physics 556. The flow tree formula for Donaldson-Thomas invariants of quivers with potentials 557. MSC 558. Virtual neighborhood technique for moduli spaces of holomorphic curves 559. Oulipian Mathematics 560. On the dynamics of inverse magnetic billiards 561. -algebras, Generalized Geometry, and Tensor Hierarchies 562. Moduli spaces of generalized hyperpolygons 563. The cohomology of the elliptic tangent bundle 564. Deformation quantization and homological reduction of a lattice gauge model 565. Hamiltonian chaos and differential geometry of configuration space–time 566. The geometry and DSZ quantization of four-dimensional supergravity 567. On the cohomology groups of real Lagrangians in Calabi–Yau threefolds 568. Superpositions in the quantum ensemble and Schroedingers cat 569. The differential geometry of Markov transitions in Hamiltonian Monte Carlo 570. On Legendrian products and twist spuns 571. frost: a momentum-conserving CUDA implementation of a hierarchical fourth-order forward symplectic integrator 572. Some Hermitian K-groups via geometric topology 573. Maximal Page Crossing Numbers of Legendrian Surfaces in Closed Contact 5-Manifolds 574. Capacities from the Chiu-Tamarkin complex 575. Smoothness of non-reductive fixed point sets and cohomology of non-reductive GIT quotients 576. Control of Parasitism in G-symplectic General Linear Methods 577. On the stability of compact pseudo-Kähler and neutral Calabi-Yau manifolds 578. -graded supergeometry: Differential graded modules, higher algebroid representations, and linear structures 579. Smooth Fields of Operators and Some Examples Coming from Canonical Quantization 580. Complex Lie algebroids and Finsler manifold in time-dependent fractal dimension and their associated decomplexifications 581. Symplectic Superposition Solution of Free Vibration of Fully Clamped Orthotropic Rectangular Thin Plate on Two-Parameter Elastic Foundation 582. DISCRETE CONFORMAL GEOMETRY OF POLYHEDRAL SURFACES AND ITS APPLICATION 583. Contraction centers in families of hyperkähler manifolds 584. Applications of the theory of Floer to symmetric spaces 585. A Symplectic Method of Numerical Simulation on Local Buckling for Cylindrical Long Shells under Axial Pulse Loads 586. On the Anti-invariant Cohomology of Almost Complex Manifolds 587. Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics 588. Memorial for Robert Hermann 589. Microlocal analysis and beyond 590. A mathematical analysis of Casimir interactions I: The scalar field 591. On naturality of the Ozsvath-Szabo contact invariant 592. The Standard cohomology of regular Courant algebroids 593. Twisted Neumann–Zagier matrices 594. Lagrangian cobordisms and Legendrian invariants in knot Floer homology 595. Categorical non-properness in wrapped Floer theory 596. The Geometric Structure of Symplectic Contraction (vol 2020, pg 3521, 2020) 597. Deformation theory of contact Lie algebras as double extensions 598. Notes on the convergence of low energy holomorphic strips 599. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface 600. Poisson groupoids and moduli spaces of flat bundles over surfaces 601. Geodesic behavior for Finsler metrics of constant positive flag curvature on 602. Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs 603. Symmetric and skew-symmetric complex structures 604. Asymptotic symmetries in the BV-BFV formalism 605. BHK mirror symmetry for K3 surfaces with non-symplectic automorphism 606. Orbits and Lagrangian Symmetries on the Phase Space 607. Stein’s method, heat kernel, and linear functions on the orthogonal groups 608. Construction of Explicit Symplectic Integrators in General Relativity. III. Reissner–Nordström-(anti)-de Sitter Black Holes 609. Mathematical modelling in accounting information systems 610. A geometric approach to Lie systems: formalism of Poisson-Hopf deformations 611. Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach 612. Covariant phase space for gravity with boundaries: metric vs tetrad formulations 613. Taut contact hyperbolas on three-manifolds 614. A review of Lie 2-algebras 615. Fukaya categories of surfaces, spherical objects and mapping class groups 616. Surgery on Anosov flows using bi-contact geometry 617. Stokes manifolds and cluster algebras 618. Ricci Curvature, Reeb Flows and Contact 3-Manifolds 619. Contact geometry in the restricted three-body problem 620. Quasiperiodicity and blowup in integrable subsystems of nonconservative nonlinear Schr\” odinger equations 621. ON THE GRAPH THEOREM FOR LAGRANGIAN INVARIANT TORI WITH TOTALLY IRRATIONAL INVARIANT SETS 622. Multiplicative quantum cobordism theory 623. Optimization, Complexity and Invariant Theory 624. What’s Next? The Mathematical Legacy of William P. Thurston Edited by Dylan Thurston 625. Symplectic discrete-time energy-based control for nonlinear mechanical systems 626. My research so far has been revolving around a 3-dimensional TQFT ˆZ, sometimes known as the homological blocks. To each 3-manifold decorated with a 627. ELEMENTARY DIFFERENTIAL GEOMETRY 628. Derived gluing construction of chiral algebras 629. From algebraic geometry to machine learning 630. Floer Homology: From Generalized Morse-Smale Dynamical Systems to Forman’s Combinatorial Vector Fields 631. Concise symplectic formulation for tetrad gravity 632. On the Geometry of Slow-Fast Phase Spaces and the Semiclassical Quantization 633. Free dihedral actions on abelian varieties 634. The -generations of the symplectic group 635. Degeneration of natural Lagrangians and Prymian integrable systems 636. A Family of Semitoric Systems with Four Focus–Focus Singularities and Two Double Pinched Tori 637. Integrability of Boltzmann’s discontinuous gravitational system 638. Abelian Complex Structures and Generalizations 639. WKB expansion for a Yang–Yang generating function and the Bergman tau function 640. IMTech 641. The Tools of Mechanics by E. Cartan and Classical Field Theory 642. Homogeneous para-K\ 643. Three-class association schemes from partial geometric designs 644. Charge algebra in Al (A) dSn spacetimes 645. Flapping Wing Coupled Dynamics in Lie Group Setting 646. Compact Hermitian symmetric spaces, coadjoint orbits, and the dynamical stability of the Ricci flow 647. Compact orbits of Parabolic subgroups 648. Learning adaptive regularization for image labeling using geometric assignment 649. An application of hypergeometric functions to heat kernels on rectangular and hexagonal tori and a “Weltkonstante”-or-how Ramanujan split temperatures 650. Computing Reeb dynamics on four-dimensional convex polytopes 651. Connected Fundamental Groups and Homotopy Contacts in Fibered Topological (C, R) Space 652. A geometric free field realisation for the genus-two class theory of type 653. Stable heat jet approach for temperature control of Fermi–Pasta–Ulam beta chain 654. Continuous normalizing flows on manifolds 655. Sklyanin algebras and a cubic root of 1 656. Invariance of Polarization Induced by Symplectomorphisms 657. Efficient and Reliable Algorithms for the Computation of Non-Twist Invariant Circles 658. Lagrangian configurations and Hamiltonian maps 659. Meta-nilpotent knot invariants and symplectic automorphism groups of free nilpotent groups 660. Localization of certain odd-dimensional manifolds with torus actions 661. Quantum superpositions and the measurement problem 662. Some examples of Family Floer mirror 663. The analysis of the dynamic optimization problem in econophysics from the point of view of the symplectic approach for constrained systems 664. GKM theory for orbifold stratified spaces and application to singular toric varieties 665. Motivic Hypercohomology Solutions in Field Theory and Applications in H-States 666. Geodesics in semi-Riemannian Geometry and links to General Relativity 667. Integrable hierarchy for the resolved conifold 668. Ricci curvature, group compactifications and the convexity of volume 669. Structure-Preserving Galerkin POD-DEIM Reduced-Order Modeling of Hamiltonian Systems 670. Weyl–Wigner representation of canonical equilibrium states 671. Nakano Positivity of direct image sheaves of adjoint line bundles with mild singularities 672. Local number variances and hyperuniformity of the Heisenberg family of determinantal point processes 673. Geometry and physics: where are we going? 674. Pair-of-pants decompositions of 4-manifolds diffeomorphic to general type hypersurfaces 675. Fault Diagnosis of Rolling Bearing Based on Local Mean Decomposition and Transient Extracting Transform 676. Augmentations and sheaves for links 677. Maximal Green Sequences for Triangle Products 678. Generalized geometry as a model for heterotic string theory 679. Geometric Integrators for Higher-Order Variational Systems and Their Application to Optimal Control 680. Rolling bearing fault diagnosis utilizing variational mode decomposition based fractal dimension estimation method 681. Towards an extended/higher correspondence 682. Non-displaceable Lagrangian links in four-manifolds 683. Instability of rational and polynomial convexity 684. Open topological recursion relations in genus 1 and integrable systems 685. Lagrangian submanifolds in coadjoint orbits provided with symplectic invariant structures: Subvariedades lagrangianas em órbitas coadjuntas munidas de estruturas … 686. Globally conservative solutions for the modified Camassa–Holm (MOCH) equation 687. The moment map on the space of symplectic 3D Monge-Amp\ere equations 688. Characteristic classes of Borel orbits of square-zero upper-triangular matrices 689. Kenfack–Życzkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit 690. Identifying Physical Law of Hamiltonian Systems via Meta-Learning