19 problems

Let $\mathcal N(\mathcal O)$ be the set of unipotent representations attached to a nilpotent orbit $\mathcal O$, and let $WF(\pi)$ denote the wave front set of a representation…

Let two wave fields be measured at a fixed measurement position, and let their time correlation be the correlation obtained by integrating one field against a time-shifted copy of…

Let $G$ be the group and let $\gamma$ be the element considered by the recursive algorithm, with intermediate groups $G^{i+1}$, elements $\gamma_i^{\dagger}$, depths $r_{i+1}$, and…

Let $F$ be a nonarchimedean local field, let $G$ be a reductive algebraic group over $F$, and let $\pi$ be an irreducible admissible representation of $G(F)$. Let…

Let $F$ be a nonarchimedean local field, let $G$ be a reductive algebraic group over $F$, and let $\bar{F}$ be an algebraic closure of $F$. For an irreducible admissible representa…

Let $F$ be a finite extension of $\mathbb{Q}_p$, let $G$ be a connected reductive group over $F$, and let $\pi$ be an irreducible smooth $\mathbb{C}$-representation of $G(F)$. The…

Maximal wave front partition conjecture. If $G_{n^*}=\operatorname{Sp}_{2n^*}$ or $\operatorname{O}_{2n^*}$, then

For a global Arthur parameter $\psi\in\widetilde{\Psi}_2(G_n)$, let $\widetilde{\Pi}_{\psi}(\epsilon_\psi)$ be its automorphic $L^2$-packet, and let $\underline{p}(\psi)$ be the pa…

Let $G$ be a reductive group, let $H$ be a spherical subgroup of $G$, and let $\overline{\operatorname{WF}}$ denote the wave-front set associated with the relevant representation.…

Let $F$ be a non-Archimedean local field, let $\bf G$ be an algebraic reductive group over $F$, and let $G=\bf G(F)$. For $\pi\in\operatorname{Irr}(G)$, let…

Let $F$ be a non-Archimedean local field, let $\bf G$ be an algebraic reductive group over $F$, and let $G=\bf G(F)$. Let $\bf H\subset G$ be a spherical subgroup defined over $F$,…

Let $F$) be a non-Archimedean local field, let $\bf G$ be an algebraic reductive group over $F$, let $G=\bf G(F)$, and let $\bf H\subset G$ be a spherical subgroup defined over $F$…

Consider Schrödinger equations whose real-valued potentials have quadratic growth, and let the associated classical orbit depend on the energy. Yajima's conjecture. Singularities o…

Let $\pi$ be an irreducible automorphic representation of a quasi-split classical group. Let $\mathfrak{n}^m(\pi)$ be the set of maximal nilpotent orbits in the wave-front set of…

Archimedean wave-front/Whittaker-support conjecture. The same two assertions should hold for Archimedean $F$. This would extend the established non-Archimedean comparison between w…

Largest-part conjecture. The largest part of the partition is

Morse-family conjecture. This Morse family parametrizes the wave front set of the Feynman amplitude corresponding to $\Gamma$. Moreover, the wave front sets of all $n$-point functi…

Let $t_n$ be the $n$-point distributions and let $\overline{t}_n$ denote their extensions. The wave front set $WF(\overline{t}_n)$ records the singular covector directions of an ex…

Let $M$ be a generically embedded $CR$ manifold, and let $p_0\in M$. Consider all germs at $p_0$ of $CR$ distributions on $M$, together with their $\mathcal{C}^{\infty}$ wave front…