\documentclass[aspectratio=169]{beamer}
\usepackage{amsmath,unicode-math,physics,tensor,xeCJK,bookmark}
\useoutertheme{metropolis}
\useinnertheme{metropolis}
\usecolortheme{metropolis}
\usefonttheme{professionalfonts}

\setbeamerfont{title}{size=\Large, series=\bfseries}
\setbeamerfont{author}{size=\small}
\setbeamerfont{date}{size=\small}
\setbeamertemplate{footline}{\vspace*{0.3cm}}

\makeatletter
% https://tex.stackexchange.com/q/66519
\apptocmd{\beamer@@frametitle}{\only<1>{\bookmark[page=\the\c@page,level=3]{#1}}}{}{}
\makeatother

\unimathsetup{math-style=ISO, bold-style=ISO, mathrm=sym}

\setsansfont{FiraGO}[BoldFont=* SemiBold, Numbers=Monospaced]
\setmathfont{Fira Math Regular}

\newCJKfontfamily\fontzhhans{Source Han Sans SC}
\newCJKfontfamily\fontzhhant{Source Han Sans TC}
\newCJKfontfamily\fontja{Source Han Sans}

\def\ii{\symrm{i}}
\def\pp{\symrm{\pi}}

\title{Fira Math}
\subtitle{Sans-serif font with Unicode math support}
\author{Xiangdong Zeng}
\date{2019/06/03\quad v0.3.2}

\begin{document}

\maketitle

\begin{frame}{Basic examples (I)}
\begin{itemize}
  \item Covariant derivative:
    \[
      \nabla \symbf{X} = \tensor{X}{^\alpha_{;\beta}} \pdv{x^\alpha} \otimes \dd{x^\beta}
                       = \qty(\tensor{X}{^\alpha_{,\beta}} + \Gamma^{\alpha}_{\beta\gamma} \, X^\gamma) \,
                         \pdv{x^\alpha} \otimes \dd{x^\beta}
    \]
  \item Einstein's field equations:
    \[ G_{\mu\nu} \equiv R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \]
  \item Schwarzschild metric:
    \[
      c^2 \dd{\tau}^2 = \qty(1-\frac{r_{\mathrm{s}}}{r}) \, c^2 \dd{t}^2
                      - \qty(1-\frac{r_{\mathrm{s}}}{r})^{-1} \dd{r}^2
                      - r^2 \underbrace{\qty(\dd{\theta}^2 + \sin^2 \theta \dd{\varphi}^2)}_{\dd{\Omega}^2}
    \]
  \item Einstein--Hilbert action:
    \[ S = \frac{1}{2\kappa} \int R \sqrt{-g} \dd[4]{x} \]
\end{itemize}
\end{frame}

\begin{frame}{Basic examples (II)}
\begin{itemize}
  \item Case $n=1$
    \small
    \[
      \int_0^{\frac{\pp}{2}}
        \frac{\sqrt{\frac12 \sqrt{\frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}} + \frac12}}%
            {\fourthroot{\theta^2 + \ln^2\cos\theta}} \dd{\theta}
      = \frac{\pp}{2\sqrt{\ln 2}}
    \]
  \item Generalization:
    \small\vspace{1ex}
    \[
      \begin{cases}
        \smash[t]{\displaystyle
          R_n^- = \frac{2}{\pp} \int_0^{\pp/2} \qty(\theta^2+\ln^2\cos\theta)^{-2^{-n-1}}
                  \sqrt{\frac12+\frac12\sqrt{\frac12+\cdots+\frac12\sqrt{
                        \frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}}}} \dd{\theta}
                = (\ln 2)^{-2^{-n}}} \\[3ex]
        \smash[b]{\displaystyle
          R_n^+ = \frac{2}{\pp} \int_0^{\pp/2} \qty(\theta^2+\ln^2\cos\theta)^{2^{-n-1}}
                  \sqrt{\frac12+\frac12\sqrt{\frac12+\cdots+\frac12\sqrt{
                        \frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}}}} \dd{\theta}
                = (\ln 2)^{2^{-n}}}
      \end{cases}
    \]
\end{itemize}
\end{frame}

\begin{frame}{Using with CJK fonts}
\begin{itemize}
  \item {\fontzhhans 【留数定理】全纯函数 $f$ 在若尔当曲线 $\gamma$ 上的积分为：}
    \[
      \oint_\gamma f(z) \dd{z}
      = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z).
    \]
  \item {\fontzhhant 【留數定理】全純函數 $f$ 在若爾當曲線 $\gamma$ 上的積分為：}
    \[
      \oint_\gamma f(z) \dd{z}
      = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z).
    \]
  \item {\fontja 【留数定理】ジョルダン曲線 $\gamma$ に沿う正則関数 $f$ の積分は、}
    \[
      \oint_\gamma f(z) \dd{z}
      = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z).
    \]
\end{itemize}
\end{frame}

\end{document}
