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In my talk I will discuss some new features of conformal anomaly and entanglement entropy in the presence of boundaries. The talk is based on recent papers
arXiv:1510.04566, arXiv:1601.06418 and arXiv:1604.07571

In this talk, I will talk about finite dimensional representations of quantum affine algebras. The main topics are Chari and Presslay's classification of finite-dimensional simple modules over quantum affine algebras, Frenkel and Reshetikhin's theory of q-characters of finite dimensional modules, Frenkel-Mukhin algorithm to compute q-characters, T-systems, Hernandez-Leclerc's conjecture about the cluster algebra structure on the ring of a subcategory of the category of all finite dimensional representations of a quantum affine algebra. I will also talk about how to obtain a class of simple modules called minimal affinizations of types A, B using mutations (joint work with Bing Duan, Yanfeng Luo, Qianqian Zhang).

We assess the neural mechanisms of learned associations in operant-learned behaviors. These learned associations or memories involve complex sets of highly specific information that must be stored with a high degree of resolution. In contrast, most studies to date examined low resolution neural mechanisms in whole brain areas, cell types or randomly selected neurons regardless of whether they were activated and participated in the behavior. Instead, high resolution memories are thought to be stored by alterations induced selectively within sparsely distributed patterns of neurons, called neuronal ensembles, that are selectively activated by cues relevant to the memory. We developed the Daun02 inactivation procedure with transgenic FosLacZ rats to demonstrate that different patterns of strongly activated Fos-expressing ensembles mediate different memories. Since these ensembles encode the memory, we developed methods that use (1) FACS to discover multiple molecular alterations and (2) FosGFP transgenic rats to discover multiple electrophysiological alterations that are induced only within Fos-expressing neurons. We have since developed a Fos-Tet-Cre transgenic rat system that allows us to selectively manipulate these alterations within Fos-expressing ensembles to assess whether they play a causal role in operant learned behaviors. It is our hope that a focus on the behaviorally activated ensembles that store the memories will permit more focused novel treatments of behavioral disorders.