Advances in Noncommutative Geometry

Ali Chamseddine is professor of physics at the American University of Beirut and the IHES. Prof. Chamseddine is known for his contributions to particle physics, general relativity, and mathematical physics. He is the recipient of the Humboldt research prize (2001), the TWAS Physics prize (2009), and the G. Bude Medal, College de France (2007). Caterina Consani is professor of mathematics at Johns Hopkins University since 2005. Prof. Consani's research interests include arithmetic geometry, algebraic geometry, and the connections with non-commutative geometry. She is an editorial board member of the Journal of Number Theory and of Rendiconti del Seminario Matematico della Università di Padova. Nigel Higson is Evan Pugh professor of mathematics at Penn State University. He is a specialist in noncommutative geometry. Prof. Higson was elected Fellow of the Royal Society of Canada in 2000. In 2001 he received Penn State's Atherton Award for excellence in teaching. Masoud Khalkhali is professor of mathematics at the University of Western Ontario and a recipient of the faculty scholar award and the graduate mentorship award. His research specialties include noncommutative geometry, mathematical physics, noncommutative spectral geometry, cyclic cohomology, quantum groups and Hopf algebras. Henri Moscovici is professor and Alice Woods Chair in Mathematics at Ohio State University. His areas of research include noncommutative geometry, global analysis and representation theory of Lie groups. Prof. Moscovici has received a Guggenheim Fellowship award (1995) and a Distinguished University Scholar award (2001). He was visiting professor at College de France (1986, 2004 and 2013), Sackler Scholar at Tel Aviv University (1996), Clay Mathematics Institute Scholar at Harvard University (1999), and is a Fellow of the American Mathematical Society. Guoliang Yu is the Powell Chair in mathematics and distinguished professor of mathematics at Texas A&M University. His research interests include noncommutative geometry, K-theory of operator algebras, index theory, topology and analysis of manifolds, geometric group theory. Prof. Yu serves on the editorial board of the Journal of Topology and Analysis, Journal of Noncommutative Geometry, Annals of K-Theory, and the Kyoto Journal of Mathematics.

Foreword.- A survey of spectral models of gravity coupled to matter (Chamseddine, van Suijlekom).- The Riemann-Roch strategy, complex lift of the scaling site (Connes, Consani).- The Baum-Connes conjecture: an extended survey (Aparicio et al.).- Lie groupoids, pseudodierential calculus and index theory (Debord, Skandalis).- Cyclic homology in a special world (Dundas).- Curvature in noncommutative geometry (Fathizadeh, Khalkhali).- Index theory and noncommutative geometry: a survey (Gorokhovsky, van Erp).-  Modular Gaussian curvature (Lesch, Moscovici).- Advances in Dixmier traces and applications (Lord et al.).- Commutants mod normed ideals (Voiculescu).- Quantum eld theory on noncommutative space (Wulkenhaar).- Higher invariants in noncommutative geometry (Xie, Yu).