arXiv research

New map constructed from equivariant spectra for manifold study.

We define and study the Burnside quotient Green ring of a Mackey functor. Some refinements of Dress induction theory are presented, together with applications to computation results for $K$-theory and $L$-theory of finite and infinite groups.

Generalizes CNNs on homogeneous spaces like Euclidean and spherical surfaces.

We construct for an equivariant cohomology theory for proper equivariant CW-complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structur…

The paper proves differentiability of evolution maps in Lie groups.

Study on diffeologies on locally convex spaces and smooth multiplication of distributions.

RPNN-EOFs model improves time series forecasting accuracy.

This paper establishes a mathematical framework for G-CNNs on homogeneous spaces.

Solves regularity problem for infinite-dimensional Lie groups.

Mackey showed that for a compact Lie group $K$, the pair $(K,C^{0}(K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of $K\times K$ invariant polarizations on $T^{\ast}K$. The …

Convex functions in dual Orlicz spaces are studied under specific topologies.

Functor connects Lie groupoid algebras to bornological structures.

Spatio-temporal RBF neural networks improve chaotic time series prediction.

Deep learning model simulates noisy dynamical systems without distributional assumptions.

This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein and Xu. Secondly, it is shown how this procedure is quantized by Rieffel induction…

Counterexample disproves completeness of model space forcing regularity in infinite-dimensional Lie groups.

Solves regularity problem for Lie groups with asymptotic estimate Lie algebras.

ICA accurately estimates treatment effects even with confounders.

Extends particle classification to curved space-times using groupoids.

Combines Fourier methods and RNNs for efficient time series prediction.

A hermitian algebra is a unital associative ${\mathbb C}$-algebra endowed with an involution such that the spectra of self-adjoint elements are contained in ${\mathbb R}$. In the case of an algebra ${\mathcal A}$ endowed with a Mackey-complete, locally convex topology such that the set of invertible elements is open an…

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration proce…

We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.

For the cotangent bundle $T^{*}K$ of a compact Lie group $K$, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space $L^{2}(K)$ under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state tra…

ForGAN uses GANs for probabilistic forecasting of sensory data.

Global models outperform univariate benchmarks in complex time series forecasting.

Enhances supervised learning speed with KT algorithm.

Characterizes continuity of monotone functionals in mixed topology.

Improves probability distribution compression with KT algorithm.

Compress++ speeds up distribution compression to near-linear time.

Improved convergence rates for Stein Variational Gradient Descent in finite-particle settings.

Enhanced fuzzy system predicts chaotic time series with improved accuracy.

Discrete Morse-Bott theory on CW complexes generalizes Forman's theory.

The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.

Survey of Floer theories and their connections.

New homology theory for semi-groups with specific properties.

New classes from 4D gauge theories.

Lectures on topological field theories and differential cohomology.

New theory couples Chern-Simons to matter, topological.

The paper defines strong emergence in field theories and proves it exists between certain theories.

Topological string theory derived from string geometry for non-perturbative effects.

New cohomology theory for Lie 2-algebras extends classical theory.

Researchers solve M-theory's gauge enhancement problem using advanced homotopy theory.

Unified Higgs bundle vacua from M-theory on Spin(7) spaces.

This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory and Symplectic Field Theory.

Develops Hodge theory for foliations using perturbed Laplacians.

Researchers find new $G_2$-conifolds in $M$-theory with potential field theory duals.

We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, a…