191 problems

Can the numerically observed fullRSB critical-exponent relation $a+b=1$ at the jamming transition be derived analytically from the scaling equations?

Do the one-species current marginals of type-D ASEP have the predicted Tracy–Widom long-time asymptotics despite the model’s two-species interactions?

Evaluate, for arbitrary loop angle $\alpha$ and integer harmonic $N$, … the singular integral determining the cosmic-string radiation power $P_N=32G\mu^2 I(N,\alpha)/(\pi^3N^2)$.

Determine the leading asymptotic of the largest eigenvalue of the $N$-Majorana quartic SYK Hamiltonian as $N\to\infty$.

Do the Matryoshka numbers satisfy $a_n\sim c\,n!n^4$, as conjectured in OEIS A177384, and what is the constant $c$?

If $n$ positive point charges have only nondegenerate electrostatic equilibria, can their potential have more than $(n-1)^2$ critical points?

Do the tree-level amplitudes $A_n(1^-,2^+,\ldots,n^+)$ vanish identically, or can they be nonzero in half-collinear kinematics—and if nonzero, what is their all-$n$ closed form?

Are five-body trispectrum descriptors, or any fixed finite order of atom-centered density correlations, universally sufficient to distinguish noncongruent three-dimensional atomic…

Does the zero-temperature Parisi measure for the zero-field SK model have smooth density and full support on $[0,1)$?

In a quantum mechanical system, let a semi-bounded operator be perturbed by a coupling constant, and regard the resulting partition function as a function of that coupling constant…

Let $n$ point charges be placed in Euclidean space, and consider their electrostatic field or potential away from the charges. Maxwell's conjecture. The field of $n$ point charges…

Consider a dilute homogeneous Bose gas with particle density $\rho$, interaction potential $v$, and positive scattering length $a>0$. Let the leading-order ground-state energy asym…

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…

For pseudopotentials corresponding to $1/q$-filling with small $q\in\{2,3,\dots\}$, let $\operatorname{Gap}_{nq}$ denote the excitation gap above the ground-state energy for the sy…

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…

Marzari–Vanderbilt conjecture. Global minimizers of the MV functional are exponentially localized.

Let $K$ be a knot with complement $C(K)$, and classify knots as hyperbolic when $C(K)$ is a hyperbolic 3-manifold, or non-hyperbolic when its complement admits one of the other geo…

The paper constructs a reality structure, or real form, on the Heisenberg double of $\operatorname{Fun}_{q}(SL(N,\operatorname{C}))$ for phase-valued $q$; for $N=2$, this is interp…

Let $\mu_{c,k}$, respectively $N_{c,k}$, denote the $k$-th eigenvalue of the operator $H_c+V$, not counted with multiplicity, respectively its multiplicity. Let $N$ be the number o…

The paper considers exceptional simple Lie superalgebras of polynomial vector fields and the invariant differential operators and related structures associated with them. Broadhurs…

Let $n$ be a positive integer, and consider the moduli space of $n$ BPS monopoles equipped with its $L^2$ metric. Manton's conjecture. The slow motion of $n$ BPS monopoles is well…

BFSS conjecture. The putative $M$-theory is a “suitable” limit of theories on matrix algebras.

The proposed quantum theory $X$ is defined purely algebraically, without background geometry, and has classical limit $3+1$ general relativity coupled to certain matter fields. The…

Localization conjecture. Developing the localization method might, in the long run, increase our understanding of evolution operators of integrable models.

Distinct-variable conjecture. There are no coinciding variables $x_i$.