Introduction To German Studies: The Romantics Then And Now (GMST 20) Syllabus

This course serves as an introduction to the interdisciplinary field of German Studies. German culture has played a seminal role in the history and culture of modern Europe, influencing and shaping the European spirit in all manner of ways. However, rather than survey the rich history of contributions of German-speaking people to European and world culture, this course will focus on the relatively small period of German Romanticism (during the late 18th and early 19th century). As we proceed we will ask the following questions: what is German culture? How has it been defined? What is German Romanticism? What themes permeate the German Romantic tradition? How are they like or unlike themes in other similar literary traditions? Who are some significant figures in literature, music, philosophy, visual arts, architecture, and how have they influenced subsequent generations of artists and intellectuals? In addition to answering these basic questions, we will use the Romantics as a lens to learn about German culture on a larger scale

C*-algebras and Equivalences for C*-correspondences

We study several notions of shift equivalence for C*-correspondences and the effect that these equivalences have on the corresponding Pimsner dilations. Among others, we prove that non-degenerate, regular, full C*-correspondences which are shift equivalent have strong Morita equivalent Pimsner dilations. We also establish that the converse may not be true. These results settle open problems in the literature. In the context of C*-algebras, we prove that if two non-degenerate, regular, full C*-correspondences are shift equivalent, then their corresponding Cuntz-Pimsner algebras are strong Morita equivalent. This generalizes results of Cuntz and Krieger and Muhly, Tomforde and Pask. As a consequence, if two subshifts of finite type are eventually conjugate, then their Cuntz-Krieger algebras are strong Morita equivalent. Our results suggest a natural analogue of the Shift Equivalence Problem in the context of C*-correspondences. Even though we do not resolve the general Shift Equivalence Problem, we obtain a positive answer for the class of imprimitivity bimodules.Comment: 30 pages; Results on the minimality of the Pimsner dilation added in Section