<p>The heat content of a domain, originally explored by Davies and van den Berg, is defined via the heat kernel of the heat equation. Much like the ground state energy, its significance lies in its ability to encode fundamental geometric properties.</p>
<p>In this talk, we extend these concepts to the setting of metric graphs, introducing both the heat content and its integrated counterpart, the torsional rigidity. By employing graph surgery and more refined analytical tools, we demonstrate how these bounds facilitate a novel approach to geometric inverse problems on graphs.</p>
