38 problems

For every black-hole spacetime with Hawking temperature $T_H$, the least-damped quasinormal mode with frequency $\omega_0$ satisfies…

For every integer $n\ge 2$ and every admissible marked configuration of $n$ complete pairwise disjoint timelike affine worldlines in Minkowski space, let $F_1,\ldots,F_n$ be the as…

Cartesian–Klein–Lie conjecture. The combination of Cartesian and Klein–Lie approaches based on the assumption that coordinates are often a representation space for a group action i…

Consider the local Iwatsuka model with a nonzero magnetic field $b$ satisfying minimal regularity assumptions such as those formulated in Section 2.1. Finiteness conjecture. The nu…

Uniform boundedness conjecture. There is a universal constant $B_{V_0,R_0}$ such that

Strict-hierarchy conjecture. If $q<2$, then

Completeness conjecture for the $S^n$ functional. The $S^n$ functional $Z$ is complete positive and complete finite. The conjecture occurs in the paper's discussion of extending th…

Thomas–Fermi dynamical neutrality conjecture. For every initial state $(\varphi_0,\rho_0)$ satisfying $0\leqslant\rho_0\in L^1(\mathbb{R}^3)\cap L^{5/3}(\mathbb{R}^3)$ and…

Dynamical Hartree conjecture. For every initial state $u_0\in H^1(\mathbb{R}^3)$ and every $R>0$,

Let $H_N$ be the $N$-electron atomic Hamiltonian with nuclear charge $Z\in\mathbb{N}$. Strong ionization conjecture. There is a universal constant $C>0$ such that, whenever $N>Z+C$…

Let $H_N$ be the $N$-electron atomic Hamiltonian with nuclear charge $Z\in\mathbb{N}$, and let $E_N=\inf\sigma(H_N)$. Denote by $N_c=N_c(Z)$ the largest number of electrons for whi…

Let $P_{abc}$ be a unital tensor that admits a covering system of partial algebras. A pointwise decomposition is a positive tensor rank decomposition … such that every factor $p^i$…

Let $P_{abc}$ be a unital symmetric real tensor, meaning that its indices are symmetric and its unit conditions are $P_{1ab}=P_{a1b}=P_{ab1}=\delta_{ab}$. A positive tensor rank de…

Let $\beta$ be the expansion parameter, let $a$ be the regularization parameter, and let $\psi_{a,\beta}(x)$ denote the function given by Theorem. At fixed $a$ and $x$, consider an…

Let $b_1(x,t)$ denote the first component of the modified Feynman checker amplitude at position $x$ and time $t$. Modified Feynman checker limiting-probability conjecture. The tota…

Let $a_1(x,t,u)$ denote the first component of the Feynman checker amplitude at position $x$ and time $t$ in the external field $u$, and define $u(x+1/2,t+1/2)=-1$ if both $x$ and…

A smooth forms theory is a classical theory $(\operatorname{Conf},S)$ whose configuration space $\operatorname{Conf}$ is a class of algebra-valued smooth forms. An algebraic condit…

A smooth forms theory is a classical theory $(\operatorname{Conf},S)$ whose configuration space $\operatorname{Conf}$ is a class of algebra-valued smooth forms. The fundamental-con…

Turbulent Riemann hypothesis. The analytic extension of $\zeta_{(f,g)}$ to the complex numbers has nontrivial zeroes only on the critical line

Boundary information inequality conjecture.

Symmetry-group correspondence conjecture. There is a one-to-one correspondence between symmetry groups acting on $(M,A,f)$ and stable solutions for $\psi$ in $(M,A,f)$.

Stable-symmetry characterization conjecture. Stable solutions are characterized by geometrical symmetries: there is a group of symmetries acting on the space that preserves the sol…

Probability interpretation conjecture. This quantity equals the real probability that the solution occurs.

Uniqueness and representation conjecture. The field $\psi$ is uniquely determined in $U$ by $f$, its boundary values, and those two equations. Moreover, $\psi$ can be expressed in…

Let $\hat{x}(\circ,\bullet)$ be a D-progressive four-dimensional stochastic process as defined by the forward and backward stochastic differential equations, with diffusion paramet…