[Tex/LaTex] Right positioning of school logo in title page

beamerpositioningpresentationstitles

I am writing my Ph.D defense presentation using Beamer and I have a problem. I would like to add school logo at the top center of my title page. I tried to follow suggestions reported in other similar posts but I still have some problems. Here it is what I am doing at the moment.

\documentclass{beamer}

\mode<presentation> {

\usetheme{Berlin}
\usepackage{graphicx} 
\usepackage{booktabs}
\usepackage[english]{babel}
\usepackage{tikz}
\titlegraphic{\vspace{2cm}}
\title[Essays]{\textbf{Essays}}
\institute[IMT] {
  IMT School for Advanced Studies Lucca \\
  \medskip
  \textit{nicola.devivo@imtlucca.it} % Your email address
  }
} % end mode<presentation>

\date{\today}

\begin{document}

\begin{frame}
\tikz [remember picture]
\node at
    ([yshift=2cm]current page.center)
    {\includegraphics[trim=0cm 4cm 0cm 0.5cm,  width=.5\textwidth,height=.35\textheight]{Logo.pdf}};
\titlepage
\end{frame}

\end{document}

The problem is that the logo image is too far from the top bar and not centered, hence all the other features of title page are too down in the page. As I try to trim above to reduce the space, a blank space appears on the top bar. How can I solve this problem?

Thank you very much

P.S.: This is what I obtain after following the first answer

enter image description here

I do not want my logo overlap the top bar and I do not want logo to be far away from the top bar.

Best Answer

Edited to include a new solution at the top.

Is this what you want?

\hspace{0.25\textwidth}
\tikz [ remember picture]
    \node at (current page.north)
    {\includegraphics[trim=0cm 4cm 0cm 0.5cm,  width=.5\textwidth,height=.35\textheight]{Logo.pdf}};

(My original answer)

\tikz [overlay, remember picture]
\node at
    (current page.north)
    {\includegraphics[trim=0cm 4cm 0cm 0.5cm,  width=.5\textwidth,height=.35\textheight]{Logo.pdf}};