Related papers: Variations on murmurations
We show that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topologiclal results are con- sequences of the modular invariance of elliptic operators on loop spaces. Previously we…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
The $p$--modulus ${\rm mod}_p(\mathcal{F})$ of a foliation $\mathcal{F}$ on a Riemannian manifold $M$ is a generalization of extremal length of plane curves introduced by L. Ahlfors. We study the variation $t\mapsto{\rm…
This paper describes an approach to generating looping animations using the modular flow and elliptic functions. The modular flow is a flow on lattices with many periodic orbits, and elliptic functions are meromorphic, doubly-periodic…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-functions and congruences between modular forms.
In this note we advocate the notion of variety as juxtaposed to the notion of complexity. Laminar flows are complex, turbulence is various. When the gradients reach a critical point, laminar flows are subjected to instabilities and…
Developments of this far-reaching research field are summarized from an observational point of view, mentioning important and interesting phenomena discovered recently by photometry of stellar oscillations of any kind. A special emphasis is…
Investigation on open questions about perturbation of Hermitian sequences and their spectral symbols. Results on normal sequences are also furnished.
We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.
Within the Lorentz invariant formalizm for description of neutrino evolution in electromagnetic fields and matter we consider neutrino spin oscillations in the circular polarized electromagnetic wave, the amplitude of which is a modulated…
In this article we review some recent developments in heterotic compactifications. In particular we review an ``inherently toric'' description of certain sheaves, called equivariant sheaves, that has recently been discussed in the physics…
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
We prove that all elliptic curves defined over real quadratic fields are modular.
The recent results on hadron multiplicities in heavy and light quark fragmentation, multiplicity local fluctuations and multiparticle correlations submitted to the Conference are reviewed.
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.