7 problems

Let a quantum field theory be scale invariant, meaning that it is invariant under scale transformations. Polyakov's conjecture. Under general conditions, the quantum field theory i…

Let a physical system be tuned to the critical temperature at which a second-order phase transition occurs, and let a quantum field theory describe the system. Criticality–scale-in…

Consider a scale-invariant theory and its sectors under the dilatation group. A non-scale-invariant sector is a sector that is not invariant under scale transformations. Scale-inva…

The Navier–Stokes system admits hidden symmetries obtained by combining a quasi-Lagrangian reference frame with spatial and temporal rescalings; these symmetries form a reduced par…

For $\theta>0$, let $A(\theta)\subset[0,\infty)$ be the scale-invariant random closed set arising from the limiting divisor model, and define … Positivity conjecture. If … then…

Let $m$ be any positive integer, let $F$ be a set of positions in $m$-heap Nim with labeled piles, and let $S\subseteq\mathbb{R}^m$ be open. For each $k$, let $\pi(S,k)$ denote the…

Let $F$ be a forbidden set defining an instance of CIS-Nim, and let $S ameqsubseteqmathbb{R}^3$ be open. For each $k$, let $pi(S,k)$ denote the number of $P$-positions of the form…