\documentclass[UKenglish,aspectratio=169,logotop]{beamer}
\usetheme{HFU}
\usepackage{csquotes} % Quotation marks
\usepackage{microtype} % Improved typography
\usepackage{amssymb} % Mathematical symbols
\usepackage{mathtools} % Mathematical symbols
\usepackage[absolute, overlay]{textpos} % Arbitrary placement
\setlength{\TPHorizModule}{\paperwidth} % Textpos units
\setlength{\TPVertModule}{\paperheight} % Textpos units
\usepackage{tikz}
\usepackage{pgf}
\usetikzlibrary{overlay-beamer-styles} % Overlay effects for TikZ
\usetikzlibrary{positioning} % Positioning of nodes for TikZ
\usetikzlibrary{arrows.meta} % more arrow styles
\author{Valentin Weber}
\title{Beamer example}
\subtitle{Usage of the theme \texttt{HFU}}
%\date{DD.MM.YYYY} % this is just a placeholder, use whatever format floats your boat
%\customerlogo{path-to-image} % this is just a placeholder. Appears on the right side of the title page.
\begin{document}
\section{Overview}
% Use
%
% \begin{frame}[allowframebreaks]{Title}
%
% if the TOC does not fit one frame.
\begin{frame}{Table of contents}
\tableofcontents
\end{frame}
\section{Mathematics}
\subsection{Theorem}
\begin{frame}{Mathematics}
\begin{theorem}[Fermat's little theorem]
For a prime~\(p\) and \(a \in \mathbb{Z}\) it holds that \(a^p \equiv a \pmod{p}\).
\end{theorem}
\begin{proof}
The invertible elements in a field form a group under multiplication.
In particular, the elements
\begin{equation*}
1, 2, \ldots, p - 1 \in \mathbb{Z}_p
\end{equation*}
form a group under multiplication modulo~\(p\).
This is a group of order \(p - 1\).
For \(a \in \mathbb{Z}_p\) and \(a \neq 0\) we thus get \(a^{p-1} = 1 \in \mathbb{Z}_p\).
The claim follows.
\end{proof}
\end{frame}
\subsection{Example}
\begin{frame}{Mathematics}
\begin{example}
The function \(\phi \colon \mathbb{R} \to \mathbb{R}\) given by \(\phi(x) = 2x\) is continuous at the point \(x = \alpha\),
because if \(\epsilon > 0\) and \(x \in \mathbb{R}\) is such that \(\lvert x - \alpha \rvert < \delta = \frac{\epsilon}{2}\),
then
\begin{equation*}
\lvert \phi(x) - \phi(\alpha)\rvert = 2\lvert x - \alpha \rvert < 2\delta = \epsilon.
\end{equation*}
\end{example}
\end{frame}
\section{Highlighting}
\SectionFrame
\begin{frame}{Highlighting}
Sometimes it is useful to \alert{highlight} certain words in the text.
\begin{alertblock}{Important message}
If a lot of text should be \alert{highlighted}, it is a good idea to put it in a box.
\end{alertblock}
It is easy to match the \structure{colour theme}.
\end{frame}
\section{Lists}
\begin{frame}{Lists}
\begin{itemize}
\item
Bullet lists are marked with a red box.
\end{itemize}
\begin{enumerate}
\item
\label{enum:item}
Numbered lists are marked with a white number inside a red box.
\end{enumerate}
\begin{description}
\item[Description] highlights important words with red text.
\end{description}
Items in numbered lists like \enumref{enum:item} can be referenced with a red box.
\begin{example}
\begin{itemize}
\item
Lists change colour after the environment.
\end{itemize}
\end{example}
\vspace{2ex}
\ConclusionArrow{Key messages or conclusions can be highlighted by using an arrow}
\end{frame}
\section{Effects}
\begin{frame}{Effects}
\begin{columns}[onlytextwidth]
\begin{column}{0.49\textwidth}
\begin{enumerate}[<+-|alert@+>]
\item
Effects that control
\item
when text is displayed
\item
are specified with <> and a list of slides.
\end{enumerate}
\begin{theorem}<2>
This theorem is only visible on slide number 2.
\end{theorem}
\end{column}
\begin{column}{0.49\textwidth}
Use \textbf<2->{textblock} for arbitrary placement of objects.
\pause
\medskip
It creates a box
with the specified width (here in a percentage of the slide's width)
and upper left corner at the specified coordinate (x, y)
(here x is a percentage of width and y a percentage of height).
\end{column}
\end{columns}
\begin{textblock}{0.3}(0.45, 0.55)
\includegraphics<1, 3>[width = \textwidth]{HFU-images/Logo_HFU_sw.pdf}
\end{textblock}
\end{frame}
\section{Diskussion und Fragen}
\SectionFrameAlt
\section{References}
\begin{frame}[allowframebreaks]{References}
\begin{thebibliography}{}
% Article is the default.
\setbeamertemplate{bibliography item}[book]
\bibitem{Hartshorne1977}
Hartshorne, R.
\newblock \emph{Algebraic Geometry}.
\newblock Springer-Verlag, 1977.
\setbeamertemplate{bibliography item}[article]
\bibitem{Helso2020}
Helsø, M.
\newblock \enquote{Rational quartic symmetroids}.
\newblock \emph{Adv. Geom.}, 20(1):71--89, 2020.
\setbeamertemplate{bibliography item}[online]
\bibitem{HR2018}
Helsø, M.\ and Ranestad, K.
\newblock \emph{Rational quartic spectrahedra}, 2018.
\newblock \url{https://arxiv.org/abs/1810.11235}
\setbeamertemplate{bibliography item}[triangle]
\bibitem{AM1969}
Atiyah, M.\ and Macdonald, I.
\newblock \emph{Introduction to commutative algebra}.
\newblock Addison-Wesley Publishing Co., Reading, Mass.-London-Don
Mills, Ont., 1969
\setbeamertemplate{bibliography item}[text]
\bibitem{Artin1966}
Artin, M.
\newblock \enquote{On isolated rational singularities of surfaces}.
\newblock \emph{Amer. J. Math.}, 80(1):129--136, 1966.
\end{thebibliography}
\end{frame}
\end{document}
