Ulrike Tillmann

 Søren Galatius

 Dev Sinha

This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.

Algebraic Topology: Applications and New Directions

Markus Peter

Romeo and Julia, two residential high-rises in Stuttgart, built 1954-59 and designed by Hans Scharoun (1893-1972), constitute the most original and far-reaching of the various attempts to re-design the entire "process of living" that this extraordinary protagonist of Germany's modern architecture undertook. Over decades, Scharoun had woven and extensive network of research and knowledge systems as a basis for his floor-plan designs. His unpublished writings and, even more importantly, his lectures from between 1947 and 1958 reveal the countless threads of research and discourse, which his work in residential architecture referenced and absorbed. They highlight the sometimes contradictory, yet constant renewal and consolidation of his knowledge in the field of housing. This new book, based on extensive research in collaboration with Berlin's Akademie der Künste, demonstrates how closely interlocked Romeo and Julia are with their architect's immense engagement with the topic of housing. Drawing on previously unpublished archive material held at the Akademie der Künste, the authors for the first time allow the reader an insight into Scharoun's design process. Alongside reproductions of original plans and drawings, the book features excerpts from Scharoun's unpublished text fragments. New images by Swiss architectural photographer Georg Aerni, illustrating the two towers' highly expressive appearance, round out this volume.

The Residential High-rises Romeo and Julia, 1954-1959

Hans Scharoun and the Development of Small Apartment Floor Plans

Daniel S. Freed

Sergei Gukov

Ciprian Manolescu

Constantin Teleman

This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.

Quantum Field Theory and Manifold Invariants

Ulrike Tillmann

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