Symplectic geometry Research Topics Ideas

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
691. Shift operators and connections on equivariant symplectic cohomology
692. The relation between Feynman diagrams and Kontsevich graphs in non-commutative star products
693. Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism
694. Contact Hamiltonian and Lagrangian systems with nonholonomic constraints
695. On the invariance of Welschinger invariants
696. Holomorphic anomaly equation for

697. A lift of the Seiberg–Witten equations to Kaluza–Klein five-manifolds
698. Equivariant cohomology for differentiable stacks
699. Billiard tables with rotational symmetry
700. T-duality and T-folds for point particles

Prof.Fazal Rehman Shamil (Available for Professional Discussions)
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