Related papers: Spectral gap for the Kac model with hard sphere co…

In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.

In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…

In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…

We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain. It…

We prove the analogue of the Heyde theorem for a-adic solenoids.

We show that the diffusion approximation breaks down for particle acceleration at oblique shocks with velocities typical of young supernova remnants. Higher order anisotropies flatten the spectral index at quasi-parallel shocks and steepen…

We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)

We address the issue of (quantum) black hole formation by particle collision in quantum physics. We start by constructing the horizon wave-function for quantum mechanical states representing two highly boosted non-interacting particles that…

We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static,…

We obtain bounds for the spectrum and for the total width of the spectral gaps for Jacobi matrices on $\ell^2(\Z)$ of the form $(H\psi)_n= a_{n-1}\psi_{n-1}+b_n\psi_n+a_n\psi_{n+1}$, where $a_n=a_{n+q}$ and $b_n=b_{n+q}$ are periodic…

We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in…

For a big tt-category, we give a characterization of the Telescope Conjecture (TC) in terms of definable tensor-ideals generated by homological residue fields. We formulate a stalk-locality property of (TC) and prove that it holds in the…

In this paper, we proved the Normal Scalar Curvature Conjecture and the Bottcher-Wenzel Conjecture. We also established some new pinching theorems for minimal submanifolds in spheres.

We consider the soft-wall holographic model with the linear dilaton background. The model leads to a Hydrogen-like meson spectrum which can be interpreted as the static limit with very large quark masses when the Coulomb interaction…

We show that if K is a compact spectrahedron whose set of extreme points is closed, then the operator system of continuous affine functions on K is hyperrigid in the C*-algebra C(ex(K)).

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The…

We consider four long-standing Rigidity Conjectures about synchrony and phase patterns for hyperbolic periodic orbits of admissible ODEs for networks. Proofs of stronger local versions of these conjectures, published in 2010-12, are now…

We established a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by the corresponding theorem of Green for homogeneous ideals in polynomial rings. Our theorem allows us to give…

The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied {\it analytically}. To that end, we solve the Klein-Gordon wave equation for…

We study the probability that a horizon appears when concentric shells of matter collide, by computing the horizon wave-function of the system. We mostly consider the collision of two ultra-relativistic shells, both shrinking and expanding,…