4 problems

Weak-coupling Yang–Mills mass gap conjecture. For any bare coupling constant $g\in[0,g_0[$, the spectrum of $H^g$ contains $0$ as a simple eigenvalue for the vacuum eigenstate and…

Yang–Mills mass gap conjecture. For any compact simple Lie group $G$ there exists a nontrivial Yang–Mills theory on the Minkowskian $\mathbf{R}^{1,3}$ whose quantization satisfies…

Let $S^k$ be the target sphere of radius $R$, and let $\tilde{\mathcal{L}}_{N,U}(S^k)$ be the manifold with boundary obtained by removing a tubular neighborhood…

Let the arboreal gas be defined on $\mathbb{Z}^2$, let $\beta>0$, and write $\mathbb{P}_{\beta}[i\leftrightarrow j]$ for the probability that $i$ and $j$ lie in the same tree. Let…