<p class="desc_biggest"><br /> <b>Matt Young, Utah State</b></p> <p class="desc_bigger"><br /> Title: <i>Z-hat invariants for Lie superalgebras</i></p> <p><br /> Abstract: The goal of this talk is to explain a representation theoretic approach to physicists&#39; so-called<i> Z</i>-hat invariants of 3-manifolds, as introduced by Gukov, Pei, Putrov and Vafa in the context of supersymmetric gauge theory. Specifically, we use the representation theory quantum supergroups to construct non-semisimple analogues of the modular tensor categories Reshetikhin, Turaev, Andersen and others. These categories can in turn be used to construct quantum invariants of 3-manifolds, certain limits of which recover the <i>Z</i>-hat invariants. Based on joint work with Francesco Costantino, Matthew Harper and Adam Robertson.</p> <p>&nbsp;</p>