Basic Notions seminar : Tomer Schlank - Spectra or homotopical Abelian groups

Thu, 08/11/201816:00-17:15
Speaker: Tomer Schlank
Title: Spectra or homotopical Abelian groups
Abstract: The notion of spectra is one of the most important constructions in modern algebraic topology. It appears naturally in the study of cobordism classes of manifolds, as the classification of generalized cohomology theories, as the manifestation of Algebraic K-theory, In the classification of Topological field theories, and many more. This amazing ubiquitousness of spectra can be explained by the observation that spectra can be thought of as a homotopical analog of abelian groups. Following this observation, In the last years, J. Lurie and other authors began redeveloping algebra with Spectra taking the role of abelian groups. Analogs of commutative and non-commutative rings, modules, lie-algebras, and many others developed, and many theorems where proved that are analogs of the classical case. The picture emerging is fascinating and includes new mysterious primes, generalized geometric objects and notions of rings interpolating between commutative and non-commutative rings. I'll describe the notion of spectra and relevant tools. I will assume familiarity with the notion of homotopy groups in the lecture but not more.