FIELD Math:Geometry March 15 (Fri), 2019 14:00-15:30 8101 Bhamidi, S.S Sreedhar Kim, Bumsig Learning Seminar on Motivic Realizations Of Singularity Categories and Vanishing Cycles This lecture is a continuation of the reading seminar on \cite{BRTV}. In these two lectures, the goal is to start reading Section 2 of the paper. We shall begin by recalling the definition of the category Landau-Ginzburg models ($LG$-models). We define the category of matrix factorizations and singularity category associated to an $LG$-model. Following the paper, we shall try to understand the above topics using the language of $\infty$-categories. The eventual goal is to prove an $\infty$-categorical version of {\it{Orlov's theorem}}. \begin{thebibliography}{99}\bibitem{BRTV} {\sc Anthony Blanc , Marco Robalo, Bertrand To\"{e}n, \& Gabriele Vezzosi,} {\em Motivic Realizations Of Singularity Categories and Vanishing Cycles} Journal de l'\'{E}cole polytechnique?Math\'{e}matiques (2017). \end{thebibliography}