报告人:Dr. Georg Tamme (University of Regensburg, Germany)
题目：Excision in algebraic K-theory
Zoom会议ID：863 2126 0358会议密码: 431083
Algebraic K-groups of rings or schemes are interesting invariants that appear in many different areas of mathematics. Unfortunately, computations are often hard because standard tools from homology, like homotopy invariance or certain Mayer-Vietoris sequences, are not available. The classical excision theorem of Bass, Milnor, and Murthy associates to a Milnor square of rings (a cartesian square with surjective horizontal maps) an exact sequence of algebraic K-groups starting with K_1. In this talk I will explain that this sequence extends naturally to a long exact sequence which involves a new `derived’ ring (a dga) naturally associated with the original Milnor square. In fact, this result holds more generally for any so called localizing invariant as for example topological Hochschild homology and it easily implies and improves excision results of Suslin-Wodzicki, Cortinas, and Geisser-Hesselholt. This is joint work with Markus Land.
Georg Tammestudied in Göttingen and Regensburg and did his PhD in 2010 (title of the thesis: The relative Chern character and regulators). His advisor was Prof. Guido Kings. After that he spent one year at the California Institute of Technology (Caltech) and his host there was Prof. Matthias Flach. He then returned to Regensburg where he did his habilitation in 2017 (title of the habilitation thesis: K-theory and regulators: Analytic and homotopical methods). From April to September 2017 he was a substitute professor at the University of Munich and since October 2020 he is a substitute professor at the University of Leipzig.His research interest includes arithmetic and algebraic geometry, homotopy theory; in particular, algebraic K-theory, regulators, differential algebraic K-theory, algebraic K-theory of ring spectra, derived algebraic geometry, motivic homotopy theory. He has published nice papers in good journals such as Ann. of Math., Invent. Math., Adv. Math., Compos. Math. and J. Geom. Phys.
童纪龙 唐 舜 陈红星
首都师范大学 数学科学学院 交叉科学研究院