Related papers: On Neeman's gradient flows

We introduce a new parabolic flow deforming any Riemannian metric on a spin manifold by following a constrained gradient flow of the total scalar curvature. This flow is built out of the well-known Dirac-Einstein functional. We prove local…

The real and imaginary part of any Abelian differential on a compact Riemann surface define two flows on the underlying compact orientable $C^\infty$ surface. Furthermore, these flows induce an interval exchange transformation on every…

We examine the proposal by Grabowska and Kaplan (GK) to use the infinite gradient flow in the domain-wall formulation of chiral lattice gauge theories. We consider the case of Abelian theories in detail, for which L\"uscher's exact…

A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show…

The gradient flow equation is derived in four-dimensional N=1 supersymmetric Yang-Mills theory in terms of the component field of the Wess-Zumino gauge. We show that the flow-time derivative and supersymmetry transformation that is naively…

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described…

Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…

In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology…

Let f:\Sigma_1 --> \Sigma_2 be an area preserving diffeomorphism between compact Riemann surfaces of constant curvature. The graph of f can be viewed as a Lagrangian submanifold in \Sigma_1\times \Sigma_2. This article discusses a canonical…

This study focuses on a Wasserstein-type gradient flow, which represents an optimization process of a continuous model of a Deep Neural Network (DNN). First, we establish the existence of a minimizer for an average loss of the model under…

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…

We develop a non-abelian, gauge-theoretic framework for the Schwarzian derivative and for second-order differential equations on Riemann surfaces. As applications, we extend Dedekind's Schwarzian approach to elliptic periods to generic…

We construct geometric examples of N-differential graded algebras such as the algebra of differential forms of depth $N$ on an affine manifold, and $N$-flat covariant derivatives.

We consider the closed orbit structure of generic gradient flows of Morse closed 1-forms. The torsion of a chain homotopy equivalence between the Novikov complex and the completed simplicial chain complex of the universal cover detects the…

We propose a supersymmetric gradient flow in ${\cal N}=1$ SQCD in four dimensions. The flow equation is derived in the superfield formalism and is also given for component fields of the Wess-Zumino gauge in a gauge covariant manner. We find…

Using spectral flow, we provide a proof of [11, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of unitary minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction…

We discuss $(K,N)$-convexity and gradient flows for $(K,N)$-convex functionals on metric spaces, in the case of real $K$ and negative $N$. In this generality, it is necessary to consider functionals unbounded from below and/or above,…

The aim of this paper is to give an overview and to compare the different deformation theories of algebraic structures. We describe in each case the corresponding notions of degeneration and rigidity. We illustrate these notions with…

Let $V$ be a $6$-dimensional complex vector space with an involution $\sigma$ of trace $0$, and let $W \subset \Sym^2 V^\vee$ be a generic $3$-dimensional subspace of $\sigma$-invariant quadratic forms. To these data we can associate an…

The nef cone volume appeared first in work of Peyre in a number-theoretic context on Del Pezzo surfaces, and it was studied by Derenthal and co-authors in a series of papers. The idea was subsequently extended to also measure the Zariski…