Related papers: Variations on murmurations
We survey recent developments on the Restriction conjecture.
In this paper, we extend the method developed in [17, 18] to curves in the Minkowski plane. The method proposes a way to study deformations of plane curves taking into consideration their geometry as well as their singularities. We deal in…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
The change of conformal moduli of polygonal quadrilaterals under some geometric transformations is studied. We consider the motion of one vertex when the other vertices remain fixed, the rotation of sides, polarization, symmetrization, and…
Searches for new physics using muons are reviewed. Particular attention is paid to muon number non-conserving processes, like the decay muon-->e+gamma and muon-electron conversion in muonic atoms. Also, experimental determinations and…
Recently, there is an explosive growth of activities to understand stringy properties of orbifolds. In this article, we survey some of recent developments.
Theory of laminated turbulnece includes continuous layer of turbulence (statistical description, kinetic equations, Zakharov-Kolmogorov spectra, etc) AND discrete layer of turbulence (isolated groups of interacting waves, no…
The problem of normalisation of the modular forms in modular invariant lepton and quark flavour models is discussed. Modular invariant normalisations of the modular forms are proposed.
We give infinitely many new isomorphisms between moduli spaces of bundles on local surfaces and on local Calabi--Yau threefolds.
We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.
Via simulation, we discover and prove curious new Euclidean properties and invariants of the Poncelet family of harmonic polygons.
The paper collects different approaches and viewpoints on bilinear forms and hermitian forms around isolated hypersurface singularities. It gives the relations between them in precise formulas. It does not contain new results.
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.
In the recent development in a various disciplines of physics, it is noted the need for including the deformed versions of the exponential functions. In this paper, we consider the deformations which have two purposes: to have them like…
Some recent progress towards understanding the cohomology of moduli spaces of curves is described. Madsen and Weiss have given a proof of a generalisation of Mumford's conjecture on the stable cohomology of these moduli spaces M_g, and…
We discuss some research problems on affine monomial curves, from the perspective of computation.
We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces of curves.
We describe our recent work on deformations of hyperelliptic curves by means of integrable hierarchy of hydrodynamic type (nlin.SI/0205012). We also discuss a further extension to the case of non-hyperelliptic curves.
We present theoretical and numerical evidence for a random matrix theoretic approach to a conjecture about vanishings of quadratic twists of certain L-functions
This is a note in which we first review symmetries of moduli spaces of stable meromorphic connections on trivial vector bundles over the Riemann sphere, and next discuss symmetries of their integrable deformations as an application. In the…