The geometry of the universal hyperKaehler implosion for SU(n) is explored. In particular, we show that the universal hyperKaehler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a gauge theoretic approach to hyperKaehler implosion.
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16 results for “implosion”
Study of symplectic and Poisson reduction, proposing Poisson implosion.
problem Understanding and generalizing symplectic reduction to Poisson manifolds.
method Recalled and reviewed symplectic and Poisson reduction, proved cross-section theorem for Poisson manifolds.
result Generalized Guillemin-Sternberg theorem for Poisson manifolds, identified Poisson transversals.
Survey and generalization of implosion and contraction in symplectic and hyperkähler geometry.
problem Exploring implosion and contraction in symplectic and hyperkähler geometry.
method Survey and extension of implosion construction to general reductive groups, interpretation in Moore-Tachikawa category, generalization of contraction construction.
result Generalization of implosion and contraction concepts to hyperkähler and complex symplectic situations.
We use Nahm data to give a description of a candidate for the universal hyperkahler implosion with respect to a compact Lie group
We introduce an analogue in hyperkahler geometry of the symplectic implosion, in the case of SU(n) actions. Our space is a stratified hyperkahler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.
We study the geometry of the twistor space of the universal hyperkaehler implosion Q for SU(n). Using the description of Q as a hyperkaehler quiver variety, we construct a holomorphic map from the twistor space Z_Q of Q to a complex vector bundle over P^1, and an associated map of Q to the affine space R of the bundle'…
Network Implosion: Effective Model Compression for ResNets via Static Layer Pruning and Retrainingcs.LG
Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this pro…
We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. As Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient, this allows one to …
The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.
problem Understanding the deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds.
method Introduces a generalized Hamiltonian deformation theory and constructs a topological quantum field theory.
result Shows that the imploded cross section of the double $D(G)_\imp$ deforms to the implosion of the cotangent bundle $T^*G_\imp$.
Let be a compact group. For a symplectic quotient of a compact Hamiltonian Kähler -manifold, we show that the induced complex structure on is locally invariant when the parameter varies in . To prove such a result, we take two different approaches: (i) by using the complex geom…
In this work, sequence-to-sequence (seq2seq) models, originally developed for language translation, are used to predict the temporal evolution of complex, multi-physics computer simulations. The predictive performance of seq2seq models is compared to state transition models for datasets generated with multi-physics cod…
We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension with a tri-Hamiltonian action of a torus of dimension , without any assumption on the finiteness of the Betti numbers. As a result we find that the hyp…
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, t…
Introduces a new method for symplectic reduction along submanifolds.
problem Symplectic reduction in various geometric categories.
method Uniform approach to symplectic reduction in smooth manifolds, complex analytic spaces, and algebraic varieties.
result Generalizes and encompasses various known reduction techniques.
Inertial confinement fusion (ICF) experiments are designed using computer simulations that are approximations of reality, and therefore must be calibrated to accurately predict experimental observations. In this work, we propose a novel nonlinear technique for calibrating from simulations to experiments, or from low fi…
Identifying Entangled Physics Relationships through Sparse Matrix Decomposition to Inform Plasma Fusion Designphysics.plasm-ph
Sparse matrix decomposition identifies key design variables for ICF experiments.
problem Improving predictive capability of ICF simulation codes through better understanding of design inputs and outcomes.
method Sparse Principal Component Analysis (SPCA) and Random Forest (RF) surrogate model.
result Identified clusters of design variables related to physical processes, revealing important variables not previously considered.