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Events happening on October 4, 2018

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Oct. 04, 2018 5pm (Math 350)	Krisztina Dearborn X Join us to practice introducing yourself at a career fair or your research elevator pitch in a stress-free, low-stakes environment. Then (if applicable) print off copies of your current resume, walk over to the Fall Technology Career Fair at the UMC (11am-4pm) with confidence, and put your practice to use. Career Fair Introductions and Research Elevator Pitches
Oct. 04, 2018 12pm (Math 350)	Noncomm Geometry Boris Tsygan (Northwestern University) X We will show that the p-adically completed periodic cyclic complex of a differential graded algebra over Z is a homotopy crystal, i.e. such complexes are canonically (up to all higher homotopies) isomorphic for any two algebras that are the same modulo p. Periodic cyclic complex as a homotopy crystal. Sponsored by the Meyer Fund
Oct. 04, 2018 12pm (MATH 350)	Ulam B. Tsygan (Northwestern University) X We will show that the p-adically completed periodic cyclic complex of a differential graded algebra over Z is a homotopy crystal, i.e. such complexes are canonically (up to all higher homotopies) isomorphic for any two algebras that are the same modulo p. Periodic cyclic complex as a homotopy crystal. Sponsored by the Meyer Fund
Oct. 04, 2018 2pm (MATH 350)	Functional Analysis Alexander Mundey (University of Wollongong) X Given a homeomorphism of a space X the associated crossed product of C(X) by the integers encodes the dynamics. However, if we are given multiple self-mappings of X it becomes less clear what the natural dynamical C-algebra to associate is. In this talk I will introduce Cuntz-Pimsner algebras, which can be thought of as a crossed product by a C-correspondence. I will explain how they can be used to encode the dynamics of certain multivariable dynamical systems, and how the K-theory of these algebras captures certain dynamical features. This talk is based primarily on Kajiwara and Watatani's work on C*-algebras associated to iterated function systems, but also relates to the work of Davidson, Katsoulis, and others on tensor algebras for multivariable dynamics. Multivariable dynamics and Cuntz-Pimsner algebras
Oct. 04, 2018 4pm (Math 350)	Noncomm Geometry Dan Freed (University of Texas at Austin) X There are many mathematical problems in which we can trade symmetry information for a parametrized family, and then extract information from the geometry of that family. In this talk we focus on this equivariance-to-families principle in differential geometry, where in joint work with Mike Hopkins we use abstract homotopy theory to develop a mathematical theory. We then describe some applications to equivariant Chern-Weil theory and to the geometry of families of Dirac operators. (An application to condensed matter physics is the subject of a talk on Friday in the physics department.) The Equivariance-to-Families Principle

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