Mathematics Problem Archive

Give a mathematically precise meaning to an exact formula comparable to Onsager's formula for the two-dimensional Ising model, and prove or disprove t...

Find an asymptotic expression for the splitting of the separatrix of a quasiperiodically forced pendulum in the regime where the perturbation series i...

For the Edwards-Anderson Ising spin glass on $\mathbb{Z}^d$ with i.i.d. mean-zero finite-variance nearest-neighbor couplings, prove or disprove the ex...

Give a mathematically rigorous formulation and justification of the nuclear shell model....

Prove that, as the number of nuclei tends to infinity, the ground state of some neutral system of nuclei and electrons approaches a periodic limit, es...

Random point processes corresponding to $\beta$-ensembles, or, equivalently, log gases at inverse temperature $\beta$, are defined for arbitrary $\bet...

The fact that RMT, and the Tracy-Widom distributions, arise in so many problems in so many different areas leads one to the following question: how ca...

Consider the Korteweg--de Vries (KdV) equation u_t + u u_x + u_{xxx} =0 with initial data u(x, t=0) = u_0(x),\qquad x\in \mathbb{R}. In the 1970's, Mc...

In 1999, J. All these early examples were ``integrable'' in the sense that certain powerful algebraic tools, e.g., determinantal particle systems, the...

Initial boundary value problems for integrable systems in $1+1$ dimensions are of great interest. It turns out, however, that in Fokas' approach the g...

Solutions of the Cauchy problem for linear dispersive equations can be expressed in terms of Fourier integral operators. This is a very challenging pr...

In 2002, P. Zhou analyzed the behavior of solutions of the Cauchy problem for perturbations of the defocusing NLS equation i u_t + u_{xx}- 2|u|^2 u - ...

Give a rigorous explicit solution of the fixed-frequency scalar-wave diffraction problem for two finite slits in the plane, including asymptotics of t...

Determine whether there exist bound entangled bipartite quantum states with negative partial transpose....