7 problems

Let $X$ be a compact manifold with a one-codimensional foliation ${\mathcal F}$ and an ${\mathcal F}$-compatible flow $\phi$. Assume that the fixed points and periodic orbits are n…

Let $\Gamma$ be a Fuchsian group, let $\Sigma$ be a double coset of $\Gamma$, and let $X$ be a $\Gamma$-conjugacy class contained in $\Sigma$. For $M\in X$, define the discriminant…

The local-global multiplicity conjecture. If $t\asymp X$ is admissible, then

Let $\Gamma(2)'$ be the commutator subgroup of $\Gamma(2)$, and let $\operatorname{Tr}(\Gamma(2)')$ denote its trace set. The commutator width of an element is the minimum number o…

Let $I(f)$ be the trace-formula distribution for a test function $f$, and let $I_{geom}(f)=m_{geom}(\theta_f)$ be its geometric expansion. Define $I_{spec}(f)$ by the cuspidal spec…

Let $(G,X)$ be a Shimura datum with reflex field $E$, let $K=K_pK^p\subset G(\mathbb A_f)$ be neat with $K_p$ hyperspecial at a prime $p$ coprime to $\lambda$, and let…

Let $G$ be the reductive group under consideration, let $\pi$ be a regular discrete series representation of $G(\mathbb{R})$, and let $e_{\pi}$ denote the stable cuspidal test func…